Publications

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Publications of Rolando Rebolledo

Table of contents

A. Complete list of Publications

  • Published research papers
  • Published books
  • Others

B. Publications classified by fields

  • General Theory of processes
  • Statistics
  • Quantum Physics
  • Engineering Applications
  • Probability
  • Philosophy and History

A. Complete list of Publications

Published research papers

  1. Introducción a la Teoría de Operadores Diferenciales Aleatorios Ordinarios.Tesis. Depto. de Matemáticas de la Facultad de Ciencias Físicas y Matemáticas, U. de Chile (1969).
  2. Présentation de la Théorie du Signal à l’aide des Mesures Cylindriques.(in collaboration with Denis de BRUCQ). Revue du CETHEDEC (1er.trim.1971).
  3. Convergence en loi des Martingales Continues.C.R. Acad. Sci. Paris 282,sér.A (1976),483-485.
  4. Remarques sur la convergence en loi des martingales vers des martingales continues (1ère partie). C.R.Acad.Sci.Paris 285,sér.A (1977),464-468.
  5. Remarques sur la convergence en loi des martingales vers des martingales continues (2ème partie).C.R.Acad.Sci.Paris 285,sér.A (1977),517-520.
  6. Convergence en loi de martingales locales discontinues. C.R.Acad.Sci.Paris 287, sér.A, (1978), 27-28.
  7. Sur les applications de la Théorie des Martingales à l’étude statistique d’une famille de processus ponctuels. Proceedings Colloque de Stat. de Grenoble. Lecture Notes in Maths., Springer-Verlag, 636 (1978), 27-70.
  8. Méthodes de Martingales dans l’étude asymptotique des files d’attente. Comptes Rendus Colloque AFCET (1977).
  9. La Méthode des Martingales appliquée à l’étude de la convergence en loi de Processus. Bull.Soc.Math.de France,Mémoire 62 (1979),125 pages.
  10. Décomposition de Martingales Locales et Raréfaction des Sauts. Sém.de Probabilités XIII, U.de Strasbourg. Lect.Notes in Maths. 721 (1979),138-146.
  11. Martingales et Convergence Etroite de Mesures de Probabilités. Kybernetika,Prague,15 (1979), 1.
  12. Martingales et Convergence Etroite des Mesures de Probabilités. Thèse de Doctorat d’Etat. Université de Paris VI “Pierre et Marie Curie”, (1979), 212 pages.
  13. Sur le Théorème de la Limite Centrale pour les Martingales Locales. C.R.Acad.Sci.Paris 288,sér.A,(1979),879-882.
  14. Sur les Temps d’Arrêt et la Topologie Etroite.C.R.Acad.Sci.Paris 289 (1979),707-709.
  15. Temps d’Arrêt et conditions nécessaires et suffisantes de compacité étroite por une suite de probabilités. Rapport Univ. de Nice (1979).
  16. Central Limit Theorems for Local Martingales. Zeit. für Wahrscheinlichkeitstheorie verw. Gebiete 51 (1980),269-286.
  17. Semi-martingales et variations quadratiques. Conditions Nécessaires et Suffisantes de convergence en loi vers une Martingale Gaussienne. C.R.Acad.Sci.Paris 290, sér.A,( 1980), 815-817.
  18. Sur l’existence de solutions à certains problèmes de Semimartingales.C.R.Acad.Sci.Paris 290,sér.A,(1980),843-846.
  19. Continuous Local Martingales,Local Times and Scale Processes (with Uwe KUCHLER, Univ.Humboldt de Berlin). REBRAPE (1989), vol.3, 43-57.
  20. Sur le Domaine d’Attraction de certains Problèmes de Martingales.Proceedings 43 ISI Meeting,Buenos Aires (1981).
  21. Sobre la Dominación de Procesos. Notas Matemáticas 13,Facultad de Matemáticas, P.U.C. (1982)
  22. L’Approximation des Diffusions et les Théorèmes de la Limite Centrale. Actas del 5 SINAPE,IME-USP (1983),68-74.
  23. Weak Convergence of Semimartingales and Discretization Methods (joint work with Eckhard PLATEN, Berlin). Stochastic Processes and their Applications 20 (1985), 41-58. North Holland.
  24. Topologie Faible et Meta-stabilité. Sém. de Probabilités XXI,Lect. Notes in Maths. 1247 Springer-Verlag (1987),544-562.
  25. Weakening the Skorokhod’s Topology. Theory of Probability and Appl. [Teoria Veroiatnosteii i primeneniia]n 1 (1987),170-172.
  26. Maximum Entropy selection of solutions to Ill-posed Martingale Problems. Bernoulli, Vol.2, VNU Press,(1987), 67-70.
  27. Funcionales Convexos sobre los Sistemas Dinámicos Estocásticos. Actas del 16 Coloquio Brasileiro de Matemática (1987)
  28. Pseudotrajectories and Stability Problems for Stochastic Dynamica Systems. Lecture Notes in Maths. 1412 (1989), Springer, Proceedings of the International Seminar on Stability Problems for Stochastic Models organized by the USSR Academy of Sciences, V.V.Zolotarev and V.V.Kalashnikov editors .
  29. Diffusion Processes associated to a Laser Model (1990),(with J.Retamal and C. Saavedra). Journal of Mathematical Physics 33, 826–831.
  30. Stochastic Analysis approach to the Laser model (1990) (with J.Retamal and C. Saavedra). in Contribuciones Científicas y Tecnológicas USACh.,167-171.
  31. The role of Weak Topologies in Stochastic Mechanics (1991). Contribuciones en Prob. y Est. Mat., Caracas, Ed. Bernoulli, núm.3 (1992), 43-60
  32. Sur la régularité des trajectoires d’un flot non adapté (1991). Comptes Rendus de l’Académie des Sciences de Paris, t.313, sér.I, 407-409.
  33. Sur la Convergence d’Intégrales Anticipatives (1991). (joint work with G.BOBADILLA and E. SAAVEDRA), “Séminaire de Proba. XXVI” Lect. Notes in Maths. 1526, 505-513.
  34. Les Principes d’Invariance en Probabilité sur l’espace de Wiener (1991), “Sém. Proba. XXVI”, Lect. Notes in Maths. 1526, Springer,501-504.
  35. A Random Field approach to weak convergence of processes (1993). (joint work with L. G. Gorostiza).“Statistics and Probability Letters” 18, 49–55.
  36. Sur l’entropie spectrale et le temps de séjour quantique (1993). (joint work with C. FERNANDEZ).C.R. Acad.Sci. Paris, t.316, Série I,569–572.
  37. On Quantum Resonance (1993). (joint work with C. Fernández).Quantum Probability, vol.VIII, 165–188.
  38. Entropy Functionals in Quantum Probability. “Aportaciones Matemáticas”, Soc. Matemática de México, n. 7, (1992), 13-36.
  39. Changing time in the Functional Central Limit Theorem (1994). Stability Problems for Stochastic Models, TVP/VSP,V.M. Zolotarev (ed.), 239–246.
  40. Quantum Flows Associated to Master Equations in Quantum Optics (1994), (joint work with Franco Fagnola and Carlos Saavedra). “Journal of Mathematical Physics”, 35,1–12.
  41. Pricing via Anticipative Stochastic Calculus (1994), (joint work with E. Platen). Advances in Applied Probability , Vol.26, Number 4,1006–1021.
  42. Sur les temps moyen de séjour quantique (1994), (joint work with L. Accardi, C. Fernández, H. Prado).C.R.Acad. Sci. Paris, t.319, sér.I, 723–726.
  43. Un modelo estocástico para asignar precios de bonos (1994), Estudios de Economía, U.Ch., vol.21, núm. 21, 91–104.
  44. Stochastic simulation of street lamps operation (1995), (joint work with S. Ríos, M. Matus and R. Trigo). Transactions IEEE, 95SM, 588-4 PWRS, 1–7.
  45. Sur les semigroupes dynamiques quantiques (1996), Ann.Math.Blaise Pascal 3, No. 1, 125–142.
  46. An ergodic theorem in Quantum Optics (1996), (joint paper with F. Fagnola), Proceedings of the Univ. of Udine Conference in honour of A. Frigerio, Editrice Universitaria Udinese, pp. 73–86, 1996.
  47. Sur l’approche de l’équilibre au moyen des flots quantiques (1995),(joint paper with F. Fagnola), C.R.Acad.Sci.Paris, sér. I,t.321, 473–476.
  48. Principles for modelling financial markets (1996), (joint work with E. Platen), J.Appl.Proba., vol. 33,601–613.
  49. On the recurrence of Quantum Dynamical Semigroups, (1997). Proc. ANESTOC’96, World Scientific Pub., 130–141.
  50. Reduction of noise by squeezed vacuum, (1997), (joint work with F.Fagnola and C.Saavedra). Proc. ANESTOC’96, World Scientific Pub., 59–69.
  51. Classical Limit Theorems related to Quantum Phase, (1998), (joint work with F. Fagnola). Open Systems and Information Dyn. 5, 289–301.
  52. The approach to equilibrium of a class of Quantum Dynamical Semigroups (1998), (joint paper with F. Fagnola), Inf.Dim.Anal.Q.Proba. and Rel. Topics, Vol.1, No.4, 1-12.
  53. A view on Stochastic Differential Equations derived from Quantum Optics, (joint paper with F. Fagnola), “Aportaciones Matemáticas de la Soc. Mexicana de Mat.”, Modelos Estocásticos, vol.14,193-214, 1998.
  54. On the Mean Quantum Sojourn Time, (joint paper with L.Accardi, C.Fernández, H.Prado), Open Systems and Inf. Dynamics Vol. 6, 227-240, 1999.
  55. The Wave Map of Feller Semigroups, In:“Stochastic analysis and mathematical physics ”(Santiago, 1998), Birkhäuser Boston, (2000), 109-121.
  56. Entropy Functional and Resonant Pure States, (joint work with C. FERNANDEZ), ‘”Notas de la Soc. de Matemática de Chile”, 22–37, 2001.
  57. On the existence of invariant states for quantum dynamical semigroups (joint work with F. Fagnola). J.Math.Phys. 42, 1296-1308, 2001.
  58. Complete positivity and Open Quantum Systems. Stochastic Analysis and Mathematical Physics (Lisbon, 1999), Prog. Prob. vol. 50 Birkhäuser Boston,101-132, 2001.
  59. Entropy functional and resonant pure states (joint work with C. Fernández). Notas Soc. Mat. Chile (N.S.) No. 1 (2001), 22–37.
  60. Quantum Markov Semigroups and their stationary states (joint work with F. Fagnola), “Stochastic analysis and mathematical physics ”, Birkhäuser Basel ISBN 3-7643-6997-3, 77-128, 2003.
  61. Subharmonic projections for a Quantum Markov Semigroup, (joint article with F. Fagnola).J.Math.Phys. 43, 1074-1082, 2002.
  62. Quantum Interacting Particles related to the Exclusion Process,“Aportaciones Matemáticas”, Sociedad de Matemáticas Mexicana, vol.16, 271-293, 2001.
  63. Some results on invariant states for quantum Markov semigroups, (joint paper with F.  Fagnola), Lect. Notes in Pure and Appl.Math., Dekker, N.Y., 197-208, 2002.
  64. Lectures on the qualitative analysis of Quantum Markov Semigroups,(joint article with F. Fagnola),Quantum Probability Communications, QP-PQ, vol. XIV, 197-239, 2002.
  65. Transience and Recurrence of quantum Markov semigroups, (joint article with F. Fagnola), Probability Theory and Related Fields, Springer, vol. 126, 289-306, 2003.
  66. Limit Problems for Quantum Dynamical Semigroups-inspired from Scattering Theory. Quantum Probability Communications QP-PQ, vol.XII, 139-172, 2003.
  67. Open quantum systems and classical trajectories. In Stochastic analysis and mathematical physics (SAMP/ANESTOC 2002), pages 141–164. World Sci. Publishing, River Edge, NJ, 2004.
  68. Decoherence of quantum Markov semigroups. Ann. Inst. H. Poincaré Probab. Statist., 41(3):349–373, 2005.
  69. A view on decoherence via master equations. Open Syst. Inf. Dyn., 12(1):37–54, 2005.
  70. Complete Positiviy and the Markov structure of Open Quantum Systems, in Open Quantum Systems II, Lecture Notes in Math. 1882, 149–182, 2006.
  71. Notes on the qualitative behavior of Quantum Markov Semigroups (joint publication with Franco Fagnola), in Open Quantum Systems III, Lecture Notes in Math. 1883, 161–204, 2006.
  72. Regularity of solutions to Linear Stochastic Schrödinger Equations, (joint paper with C.  Mora), Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 10, No. 2, 237-259, 2007).
  73. On non-Markovian Time Evolution in Open Quantum Systems, (joint paper with A. Kossakowski). Open Systems & Information Dynamics 14, 3 (Sep. 2007), 265-274. DOI= http://dx.doi.org/10.1007/s11080-007-9051-5.
  74. Basic properties of non-linear stochastic Schrödinger equations driven by Brownian motions, (joint paper with C.  Mora), Ann. Applied Probability, 18,2 (2008), 591–619.
  75. Adiabatic limits and quantum decoherence, (joint paper with D. Spehner), Proceedings of Stochastic Analysis in Mathematical Physics, World Sci., ISBN-13 978-981-279-154-2, (2007), 94–108
  76. On Completely Positive Non-Markovian Evolution of a d-level System, (joint paper with A. Kossakowski), Open Systems & Inf. Dyn. 15, 2 (2008), 135–141.
  77. Algebraic Conditions for Convergence of a Quantum Markov Semigroup to a Steady State, (joint paper with F. Fagnola), Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 11, 3, (2008), 467–474.
  78. On non-Markovian time evolution in open quantum systems, (joint paper with A. Kossakowski), Quantum bio-informatics, 161–169, QP–PQ: Quantum Probab. White Noise Anal., 21, World Sci. Publ., Hackensack, NJ, 2008.
  79. On the Structure of Generators for Non Markovian Master Equations, (joint paper with A. Kossakowski), Open Systems & Inf. Dyn. 16, 2-3, (2009), 259–268.
  80. Unraveling Open Quantum Systems: Classical Reductions and Classical Dilations of Quantum Markov Semigroups, Confluentes Mathematici, vol. 1, (2009), 123–167.
  81. From Classical to Quantum Entropy Production, (joint paper with F. Fagnola), QP–PQ: Quantum Probab. White Noise Anal., World Sci. Publ., vol. 25, (2010), 245–261.
  82. The Decoherence-free subalgebra of a Quantum Markov Semigroup with unbounded generator, (joint paper with A. Dhahri and F. Fagnola), Inf. Dim. An. Quantum Probability and Related Topics, vol. 13, number 3, 413-433, 2010.
  83. Stochastic Processes. In International Encyclopedia of Statistical Science, Springer Reference, Lovric, Miodrag (Ed.) 1st Edition., 2010, ISBN: 978-3-642-04897-5, 2010.
  84. Can one validly use classical statistical inference in Open Quantum Systems? , (joint paper with M. Arenas), Open Systems and Inf. Dynamics, vol. 17, number 4, 311-330, 2010.
  85. Gaussian and cosine transforms, (joint paper with C. Lizama). Comm. on Stochastic Analysis, vol. 4, number 4, 541-551, 2010.
  86. The Decoherence-free Subalgebra of a Quantum Markov Semigroup on B(h), (joint paper with A.Dhahri and F.Fagnola), QP-PQ, vol XXVII, World Scientific Singapore, 131-147, 2011.
  87. Measurements and consistent families of Quantum Channels, (joint paper with Yves Le Jan), Open Systems & Inf. Dyn. 18, 3, (2011), 235-251.
  88. Equilibrium Analysis of a Dissipative Fermion System, in Spectral Days 2010, Operator Theory: Advances and Applications, vol. 224, 2012, 277-299.
  89. On a class of Non Markovian Langevin Equation, (joint paper with Carlos Lizama). Open Systems & Information Dynamics Vol. 20, No. 4 (2013) 1350016 (17 pages) DOI:10.1142/S1230161213500169.
  90. Dealing with uncertainty in Earthquake Engineering: a discussion on the application of the Theory of Open Dynamical Systems, (Joint paper with P. Quintana and G. Allan). Obras y Proyectos UCSC, vol. 14, 74-84, 2013.
  91. Decoherence-free subspaces of a quantum Markov semigroup. J. Math. Phys. 55, 112201 (2014); http://dx.doi.org/10.1063/1.4901009, (joint paper with J. Agredo and F. Fagnola)

92. Entropy Production for Quantum Markov Semigroups (joint paper with F. Fagnola). Commun. Math. Phys. 335, 547–570 (2015). Digital Object Identifier (DOI) 10.1007/s00220-015-2320-1.

Published books

1. Lectures in Probability and Statistics (editor). Lect.Notes in Maths. 1215(1986).
2. Ecuaciones Diferenciales Ordinarias, (undergraduate textbook written in collaboration with Claudio Fernández), 2nd.edition Alfa-Omega, 1999.
3. ANESTOC’96, Stochastic Analysis and Mathematical Physics (editor), Proceedings of the Second International Workshop, World Scientific Publishers, (1998).
4. ANESTOC’98,Stochastic Analysis and Mathematical Physics (editor), Proceedings of the Third International Workshop, Birkhaüser-Verlag, Boston, (2000).
5. ANESTOC’2000,Stochastic Analysis and Mathematical Physics (editor), Proceedings of the Fourth International Workshop, Birkhaüser-Verlag, Boston, (2002).
6. ANESTOC’2002,Stochastic Analysis and Mathematical Physics (coeditor with J. Rezende and J.C. Zambrini), Stochastic analysis and mathematical physics (SAMP/ANESTOC 2002), River Edge, NJ, 2004. World Scientific Publishing Co. Inc.
7. Quantum Probability and Related Topics, vol. XXVII, (Editors: R. Rebolledo and M. Orszag). Proceedings of the 30th Conference. World Scientific, ISBN-13 978-981-4338-73-8, ISBN-10 981-4338-73-7, Singapore, 2011.

Others

1. “Kolmogorov y su época”, Revista de la Soc. Chilena de Estadística (1988).
2. Mathematics in Latin America during the 20th Century. Gaceta de la Sociedad de Matemática de Chile, (1998).
3. “Interpoiesis e interdisciplina” En Haye, A. y Rojas C. (eds.) Actas Seminario Interdisciplina en la UC celebrado en Santiago de Chile el día 14 de Diciembre de 2011 (pp. 48-54). Vicerrectoría de Investigación. Facultad de Ciencias Sociales. Facultad de Filosofía, 2012
4. “Complejidad y Azar”, Cuadernos de Filosofía, Universidad de Concepción, no 30-31, 2012-2013.

B. Publications classified by fields

General Theory of processes

1. Introducción a la Teoría de Operadores Diferenciales Aleatorios Ordinarios. Tesis. Depto. de Matemáticas de la Facultad de Ciencias Físicas y Matemáticas, U. de Chile (1969).
2. Présentation de la Théorie du Signal à l’aide des Mesures Cylindriques.authored withcoauthored with Denis de BRUCQ). Revue du CETHEDEC (1er.trim.1971).
3. Convergence en loi des Martingales Continues.C.R. Acad. Sci. Paris 282,.A (1976),483-485.
4. Remarques sur la convergence en loi des martingales vers des martingales continues (1ère partie). C.R.Acad.Sci.Paris 285,sér.A (1977),464-468.
5. Remarques sur la convergence en loi des martingales vers des martingales continues (2ème partie).C.R.Acad.Sci.Paris 285,sér.A (1977),517-520.
6. Convergence en loi de martingales locales discontinues. C.R.Acad.Sci.Paris 287, sér.A, (1978), 27-28.
8. Méthodes de Martingales dans l’étude asymptotique des files d’attente. Comptes Rendus Colloque AFCET (1977).
9. La Méthode des Martingales appliquée à l’étude de la convergence en loi de Processus. Bull.Soc.Math.de France,Mémoire 62 (1979),125 páginas.
10. Décomposition de Martingales Locales et Raréfaction des Sauts. Sém.de Probabilités XIII, U.de Strasbourg. Lect.Notes in Maths. 721 (1979),138-146.
11. Martingales et Convergence Etroite de Mesures de Probabilités. Kybernetika,Prague,15 (1979), 1.
12. Martingales et Convergence Etroite des Mesures de Probabilités. Thèse de Doctorat d’Etat. Université de Paris VI “Pierre et Marie Curie”, (1979), 212 páginas.
13. Sur le Théorème de la Limite Centrale pour les Martingales Locales. C.R.Acad.Sci.Paris 288,sér.A,(1979),879-882.
14. Sur les Temps d’Arrêt et la Topologie Etroite.C.R.Acad.Sci.Paris 289 (1979),707-709.
15. Temps d’Arrêt et conditions nécessaires et suffisantes de compacité étroite por une suite de probabilités. Rapport Univ. de Nice (1979).
16. Central Limit Theorems for Local Martingales. Zeit. für Wahrscheinlichkeitstheorie verw. Gebiete 51 (1980),269-286.
17. Semi-martingales et variations quadratiques. Conditions Nécessaires et Suffisantes de convergence en loi vers une Martingale Gaussienne. C.R.Acad.Sci.Paris 290, sér.A,( 1980), 815-817.
18. Sur l’existence de solutions à certains problèmes de Semimartingales.C.R.Acad.Sci.Paris 290,sér.A,(1980),843-846.
19. Continuous Local Martingales,Local Times and Scale Processes (con Uwe Kuchler, Univ.Humboldt de Berlin). REBRAPE (1989), vol.3, 43-57.
20. Sur le Domaine d’Attraction de certains Problèmes de Martingales.Proceedings 43 ISI Meeting, Buenos Aires (1981).
21. Sobre la Dominación de Procesos. Notas Matemáticas 13,Fac.
Matemáticas, P.U.C. (1982)
22. L’Approximation des Diffusions et les Théorèmes de la Limite Centrale. Actas del 5 SINAPE,IME-USP (1983),68-74.
23. Weak Convergence of Semimartingales and Discretization Methods (artículo con Eckhard Platen, Berlin). Stochastic Processes and their Applications 20 (1985), 41-58. North Holland.
24. Topologie Faible et Meta-stabilité. Sém. de Probabilités XXI,Lect. Notes in Maths. 1247 Springer-Verlag (1987),544-562.
25. Weakening the Skorokhod’s Topology. Theory of Probability and Appl. [Teoria Veroia¬tnosteii i primeneniia]n 1 (1987),170-172.
26. Maximum Entropy selection of solutions to Ill-posed Martingale Problems. Bernoulli, Vol.2, VNU Press,(1987), 67-70.
27. Funcionales Convexos sobre los Sistemas Dinámicos Estocásticos. Actas del 16 Coloquio Brasileiro de Matemática (1987)
28. Pseudotrajectories and Stability Problems for Stochastic Dynamical Systems. Lecture Notes in Maths. 1412 (1989), Springer, Proceedings of the International Seminar on Stability Problems for Stochastic Models organizado por Academia de Ciencias, Rusia, V.V.Zolotarev y V.V.Kalashnikov editores .
35. A Random Field approach to weak convergence of processes (1993). (coauthored with L. G. Gorostiza).“Statistics and Probability Letters” 18, 49–55.
89. On a class of Non Markovian Langevin Equation, (joint paper with Carlos Lizama). Open Systems & Information Dynamics Vol. 20, No. 4 (2013) 1350016 (17 pages) DOI:10.1142/S1230161213500169.

Statistics

7. Sur les applications de la Théorie des Martingales à l’étude statistique d’une famille de processus ponctuels. Proceedings Colloque de Stat. de Grenoble. Lecture Notes in Maths., Springer-Verlag, 636 (1978), 27-70.
84. Can one validly use classical statistical inference in Open Quantum Systems? , (coauthored with M. Arenas), Open Systems and Inf. Dynamics, vol. 17, number 4, 311-330, 2010.

Quantum Physics

Closed systems

36. Sur l’entropie spectrale et le temps de séjour quantique (1993). (coauthored with C. Fernández ). C.R. Acad.Sci. Paris, t.316, Série I,569–572.
37. On Quantum Resonance (1993). (coauthored with C. Fernández).Quantum Probability, vol.VIII, 165–188.
38. Entropy Functionals in Quantum Probability. “Aportaciones Matemáticas”, Soc. Mate¬má¬tica de México, n. 7, (1992), 13-36.
42. Sur les temps moyen de séjour quantique (1994), (coauthored with L. Accardi, C. Fernández, H. Prado).C.R.Acad. Sci. Paris, t.319, sér.I, 723–726.
54. On the Mean Quantum Sojourn Time, (coauthored with L.Accardi, C.Fernández, H.Prado), Open Systems and Inf. Dynamics Vol. 6, 227-240, 1999.
56. Entropy Functional and Resonant Pure States, (coauthored with C.Fernández), ‘”Notas de la Soc. de Matemática de Chile”, 22–37, 2001.

Open systems

29. Diffusion Processes associated to a Laser Model (1990),(coauthored with J. Retamal y C. Saavedra). Journal of Mathematical Physics 33, 826–831.
30. Stochastic Analysis approach to the Laser model (1990) (con J. Retamal y C. Saavedra). in Contribuciones Científicas y Tecnológicas USACh.,167-171.
31. The role of Weak Topologies in Stochastic Mechanics (1991). Contribuciones en Prob. y Est. Mat., Caracas, Ed. Bernoulli, núm.3 (1992), 43-60
46. An ergodic theorem in Quantum Optics (1996), (coauthored with F. Fagnola), Proceedings of the Univ. of Udine Conference in honour of A. Frigerio, Editrice Universitaria Udinese, pp. 73–86, 1996.
50. Reduction of noise by squeezed vacuum, (1997), (coauthored with F. Fagnola and C. Saavedra). Proc. ANESTOC’96, World Scientific Pub., 59–69.
53. A view on Stochastic Differential Equations derived from Quantum Optics, (coauthored with F. Fagnola), “Aportaciones Matemáticas de la Soc. Mexicana de Mat.”, Modelos Estocásticos, vol.14,193-214, 1998.
58. Complete positivity and Open Quantum Systems. Stochastic Analysis and Mathematical Physics (Lisbon, 1999), Prog. Prob. vol. 50 Birkhäuser Boston,101-132, 2001.
66. Open quantum systems and classical trajectories. In Stochastic analysis and mathematical physics (SAMP/ANESTOC 2002), pages 141–164. World Sci. Publishing, River Edge, NJ, 2004.
72. On non-Markovian Time Evolution in Open Quantum Systems, (coauthored with A. Kossakowski). Open Systems & Information Dynamics 14, 3 (Sep. 2007), 265-274.
74. Adiabatic limits and quantum decoherence, (coauthored with D. Spehner), Proceedings of Stochastic Analysis in Mathematical Physics, World Sci., (2007), 94–108.
75. On Completely Positive Non-Markovian Evolution of a d-level System, (coauthored with A. Kossakowski), Open Systems & Inf. Dyn. 15, 2 (2008), 135–141.
77. On non-Markovian time evolution in open quantum systems, (coauthored with A. Kossakowski), Quantum bio-informatics, 161–169, QP–PQ: Quantum Probability. White Noise Anal., 21, World Sci. Publ., Hackensack, NJ, 2008.
78. On the Structure of Generators for Non Markovian Master Equations, (coauthored with with A. Kossakowski), Open Systems & Inf. Dyn. 16, 2-3, (2009), 259–268.
79. Unraveling Open Quantum Systems: Classical Reductions and Classical Dilations of Quantum Markov Semigroups, Confluentes Mathematici, vol. 1, (2009), 123–167.
80. From Classical to Quantum Entropy Production, (coauthored with F. Fagnola), QP– PQ: Quantum Probability. White Noise Anal., World Sci. Publ., vol. 25, (2010), 245–261.
81. The Decoherence-free subalgebra of a Quantum Markov Semigroup with unbounded generator, (coauthored with A. Dhahri y F. Fagnola), Inf. Dim. An. Quantum Probability and Related Topics, vol. 13, number 3, 413-433, 2010.
83. Can one validly use classical statistical inference in Open Quantum Systems? , (coauthored with M. Arenas), Open Systems and Inf. Dynamics, vol. 17, number 4, 311-330, 2010.
85. The Decoherence-free Subalgebra of a Quantum Markov Semigroup on B(h), (coauthored with A. Dhahri y F. Fagnola), QP-PQ, vol XXVII, World Scientific Singapore, 131-147, 2011.
86. Measurements and consistent families of Quantum Channels, (joint paper with Yves Le Jan), Open Systems & Inf. Dyn. 18, 3, (2011), 235-251.
87. Equilibrium Analysis of a Dissipative Fermion System, in Spectral Days 2010, Operator Theory: Advances and Applications, vol. 224, 2012, 277-299.
91. Decoherence-free subspaces of a quantum Markov semigroup. J. Math. Phys. 55, 112201 (2014); http://dx.doi.org/10.1063/1.4901009, (joint paper with J. Agredo and F. Fagnola)
92. Entropy Production for Quantum Markov Semigroups (joint paper with F. Fagnola). Commun. Math. Phys. 335, 547–570 (2015). Digital Object Identifier (DOI) 10.1007/s00220-015-2320-1.

Engineering Applications

Power Systems and Structural Engineering

44. Stochastic simulation of street lamps operation (1995), (coauthored with S. Ríos, M. Matus and R. Trigo). Transactions IEEE, 95SM, 588-4 PWRS, 1–7.
90. Dealing with uncertainty in Earthquake Engineering: a discussion on the application of the Theory of Open Dynamical Systems, (Joint paper with P. Quintana and G. Allan). Obras y Proyectos UCSC, vol. 14, 74-84, 2013.

Finance

41. Pricing via Anticipative Stochastic Calculus (1994), (coauthored with E. Platen). Advances in Applied Probability , Vol.26, Number 4,1006–1021.
43. Un modelo estocástico para asignar precios de bonos (1994), Estudios de Economía, U.Ch., vol.21, núm. 21, 91–104.
48. Principles for modelling financial markets (1996), (coauthored with E. Platen), J.Appl.Proba., vol. 33,601–613.

Probability

Classical Probability

32. Sur la régularité des trajectoires d’un flot non adapté (1991). Comptes Rendus de l’Académie des Sciences de Paris, t.313, sér.I, 407-409.
33. Sur la Convergence d’Intégrales Anticipatives (1991). (artículo conjunto con G. Bobadilla y E. Saavedra), “Séminaire de Proba. XXVI” Lect. Notes in Maths. 1526, 505-513.
34. Les Principes d’Invariance en Probabilité sur l’espace de Wiener (1991), “Sém. Proba. XXVI”, Lect. Notes in Maths. 1526, Springer,501-504.
39. Changing time in the Functional Central Limit Theorem (1994). Stability Problems for Stochastic Models, TVP/VSP,V.M. Zolotarev (ed.), 239–246.
51. Classical Limit Theorems related to Quantum Phase, (1998), (coauthored with F. Fagnola). Open Systems and Information Dyn. 5, 289–301.
55. The Wave Map of Feller Semigroups, In:“Stochastic analysis and mathematical physics ”(Santiago, 1998), Birkhäuser Boston, (2000), 109-121.
82. Stochastic Processes. In International Encyclopedia of Statistical Science, Springer Reference, Lovric, Miodrag (Ed.) 1st Edition, 2010.
84. Gaussian and cosine transforms, (coauthored with C. Lizama). Comm. on Stochastic Analysis, vol. 4, number 4, 541-551, 2010.

Quantum Probability

45. Sur les semigroupes dynamiques quantiques (1996), Ann.Math.Blaise Pascal 3, No. 1, 125–142.
47. Sur l’approche de l’équilibre au moyen des flots quantiques (1995),(coauthored with F. Fagnola), C.R.Acad.Sci.Paris, sér. I,t.321, 473–476.
49. On the recurrence of Quantum Dynamical Semigroups, (1997). Proc. ANESTOC’96, World Scientific Pub., 130–141.
52. The approach to equilibrium of a class of Quantum Dynamical Semigroups (1998), (coauthored with F. Fagnola), Inf.Dim.Anal.Q.Proba. and Rel. Topics, Vol.1, No.4, 1-12.
57. On the existence of invariant states for quantum dynamical semigroups (coauthored with F. Fagnola). J.Math.Phys. 42, 1296-1308, 2001.
59. Quantum Markov Semigroups and their stationary states (coauthored with F. Fagnola), “Stochastic analysis and mathematical physics ”, Birkhäuser Basel ISBN 3-7643-6997-3, 77-128, 2003.
60. Subharmonic projections for a Quantum Markov Semigroup, (coauthored with F. Fagnola).J.Math.Phys. 43, 1074-1082, 2002.
61. Quantum Interacting Particles related to the Exclusion Process,“Aportaciones Matemáticas”, Sociedad de Matemáticas Mexicana, vol.16, 271-293, 2001.
62. Some results on invariant states for quantum Markov semigroups, (coauthored with F. Fagnola), Lect. Notes in Pure and Appl.Math., Dekker, N.Y., 197-208, 2002.
63. Lectures on the qualitative analysis of Quantum Markov Semigroups,(coauthored with F. Fagnola), Quantum Probability Communications, QP-PQ, vol. XIV, 197-239, 2002.
64. Transience and Recurrence of quantum Markov semigroups, (joint article with F. Fagnola), Probability Theory and Related Fields, Springer, vol. 126, 289-306, 2003.
65. Limit Problems for Quantum Dynamical Semigroups-inspired from Scattering Theory. Quantum Probability Communications QP-PQ, vol.XII, 139-172, 2003.
67. Decoherence of quantum Markov semigroups. Ann. Inst. H. Poincaré Probab. Statist., 41(3):349–373, 2005.
68. A view on decoherence via master equations. Open Syst. Inf. Dyn., 12(1):37–54, 2005.
69. Complete Positiviy and the Markov structure of Open Quantum Systems, in Open Quantum Systems II, Lecture Notes in Math. 1882, 149–182, 2006.
70. Notes on the qualitative behavior of Quantum Markov Semigroups (coauthored with Franco Fagnola), en Open Quantum Systems III, Lecture Notes in Math. 1883, 161–204, 2006.
71. Regularity of solutions to Linear Stochastic Schrödinger Equations, (coauthored with C. Mora), Infinite Dimensional Analysis, Quantum Probability Related Topics, Vol. 10, No. 2, 237-259, 2007).
73. Basic properties of non-linear stochastic Schrödinger equations driven by Brownian motions, (coauthored with C. Mora), Ann. Applied Probability, 18,2 (2008), 591–619.
76. Algebraic Conditions for Convergence of a Quantum Markov Semigroup to a Steady State, (coauthored with F. Fagnola), Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 11, 3, (2008), 467–474.
80. From Classical to Quantum Entropy Production, (coauthored with F. Fagnola), QP–PQ: Quantum Probability. White Noise Anal., World Sci. Publ., vol. 25, (2010), 245–261.
81. The Decoherence-free subalgebra of a Quantum Markov Semigroup with unbounded generator, (coauthored with A. Dhahri y F. Fagnola), Inf. Dim. An. Quantum Probability and Related Topics, vol. 13, number 3, 413-433, 2010.
85. The Decoherence-free Subalgebra of a Quantum Markov Semigroup on B(h), (coauthored with A. Dhahri y F. Fagnola), QP-PQ, vol XXVII, World Scientific Singapore, 131-147, 2011.
86. Measurements and consistent families of Quantum Channels, (coauthored with Yves Le Jan), Open Systems & Inf. Dyn. 18, 3, (2011).
88. Equilibrium Analysis of a Dissipative Fermion System, in Spectral Days 2010, Operator Theory: Advances and Applications, vol. 224, 2012, 277-299.
91. Decoherence-free subspaces of a quantum Markov semigroup. J. Math. Phys. 55, 112201 (2014); http://dx.doi.org/10.1063/1.4901009, (joint paper with J. Agredo and F. Fagnola)
92. Entropy Production for Quantum Markov Semigroups (joint paper with F. Fagnola). Commun. Math. Phys. 335, 547–570 (2015). Digital Object Identifier (DOI) 10.1007/s00220-015-2320-1.

Philosophy and History

1. “Kolmogorov y su época”, Revista de la Soc. Chilena de Estadística (1988).
2. Mathematics in Latin America during the 20th Century. Gaceta de la Sociedad de Matemática de Chile, (1998).
3. “Interpoiesis e interdisciplina” En Haye, A. y Rojas C. (eds.) Actas Seminario Interdisciplina en la UC celebrado en Santiago de Chile el día 14 de Diciembre de 2011 (pp. 48-54). Vicerrectoría de Investigación. Facultad de Ciencias Sociales. Facultad de Filosofía, 2012
4. “Complejidad y Azar”, Cuadernos de Filosofía, Universidad de Concepción, no 30-31, 2012-2013.

Significant publications

1. La Méthode des Martingales appliquée à l’étude de la convergence en loi de Processus. Bull.Soc.Math.de France,Mémoire 62 (1979),125 pages.
2. Sur les applications de la Théorie des Martingales à l’étude statistique d’une famille de processus ponctuels. Proceedings Colloque de Stat. de Grenoble. Lecture Notes in Maths., Springer-Verlag, 636 (1978), 27-70.
3. Central Limit Theorems for Local Martingales. Zeit. für Wahrscheinlichkeitstheorie verw. Gebiete 51 (1980),269-286.
4. Semi-martingales et variations quadratiques. Conditions Nécessaires et Suffisantes de convergence en loi vers une Martingale Gaussienne. C.R.Acad.Sci.Paris 290, sér.A,( 1980), 815-817.
5. Weakening the Skorokhod’s Topology. Theory of Probability and Appl. [Teoria Veroiatnosteii i primeneniia]n 1 (1987),170-172.
6. Diffusion Processes associated to a Laser Model (1990),(with J.Retamal and C. Saavedra). Journal of Mathematical Physics 33, 826–831.
7. Quantum Flows Associated to Master Equations in Quantum Optics (1994), (joint work with Franco Fagnola and Carlos Saavedra). “Journal of Mathematical Physics”, 35,1–12.
8. A Random Field approach to weak convergence of processes (1993). (joint work with L. G. Gorostiza).“Statistics and Probability Letters” 18, 49–55.
9. On Quantum Resonance (1993). (joint work with C. Fernández).Quantum Probability, vol.VIII, 165–188.
10. Changing time in the Functional Central Limit Theorem (1994). Stability Problems for Stochastic Models, TVP/VSP,V.M. Zolotarev (ed.), 239–246.
11. Pricing via Anticipative Stochastic Calculus (1994), (joint work with E. Platen). Advances in Applied Probability , Vol.26, Number 4,1006–1021.
12. Sur les semigroupes dynamiques quantiques (1996), Ann.Math.Blaise Pascal 3, No. 1, 125–142.
13. Principles for modelling financial markets (1996), (joint work with E. Platen), J.Appl.Proba., vol. 33,601–613.
14. The approach to equilibrium of a class of Quantum Dynamical Semigroups (1998), (joint paper with F. Fagnola), Inf.Dim.Anal.Q.Proba. and Rel. Topics, Vol.1, No.4, 1-12.
15. On the existence of invariant states for quantum dynamical semigroups (joint work with F. Fagnola). J.Math.Phys. 42, 1296-1308, 2001.
16. Subharmonic projections for a Quantum Markov Semigroup, (joint article with F. Fagnola).J.Math.Phys. 43, 1074-1082, 2002.
17. Transience and Recurrence of quantum Markov semigroups, (joint article with F. Fagnola), Probability Theory and Related Fields, Springer, vol. 126, 289-306, 2003
18. Decoherence of quantum Markov semigroups. Ann. Inst. H. Poincaré Probab. Statist., 41(3):349–373, 2005.
19. Measurements and consistent families of Quantum Channels, (joint paper with Yves Le Jan), Open Systems & Inf. Dyn. 18, 3, (2011), 235-251.
20. Entropy Production for Quantum Markov Semigroups (joint paper with F. Fagnola). Commun. Math. Phys. 335, 547–570 (2015). Digital Object Identifier (DOI) 10.1007/s00220-015-2320-1.

Awards

  • “Presidential Chair” in Mathematics, 1995, delivered by the President of the Republic of Chile upon the advice and evaluation of an international scientific jury.
  • “Presidential Chair” in Mathematics, 1999, delivered by the Pres-ident of the Republic of Chile upon the advice and evaluation of an international scientific jury.
  • Medal of the “Pontificia Universidad Católica de Chile” for academic activities 1996.
  • Medal of the “Pontificia Universidad Católica de Chile” for academic activities 1999.