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Entropy Minimization Problems with Linear Constraints, Schrödinger Bridge and a Conditional Sanov Theorem

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Abstract

This paper accounts for Csiszar’s geometric approach to entropy minimization problems, connection with Schrödinger’s bridge and a conditional Sanov theorem.

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References

  1. R. Aebi and M. Nagasawa, “Large Deviations and the Propagation of Chaos for Schrödinger Process (Preprint).

    Google Scholar 

  2. A. Blaquière, “Controllability of a Fokker-Planck Equation, the Schrödinger System, and a Related Stochastic Optimal Control (Revised Version)”, in Dynamics and Control vol.2, no. 3, pp. 235–253, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Blaquière and M. Sigal-Pauchard, “Stochastic Control Approach to the Control of a Forward Parabolic Equation, Reciprocal Process and Minimum Entropy”, in Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems (Ed. R.F. Curtain, Honorary Eds. A. Bensoussan, J.L. Lions) Lecture Notes in Control and Information Sciences 185, Springer-Verlag: Berlin Heidelberg, pp. 476–488, 1993; Proc.10th Int. Conf. on Analysis and Optimization of Systems INRIA-Sophia-Antipolis, France, 1992.

    Google Scholar 

  4. I. Csiszar, “I-Divergence Geometry of Probability Distributions and Minimization Problems” The Annals of Probability vol. 3, no. 1, pp. 146–158, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  5. I. Csiszar, “Sanov Property, Generalized /-Projection and a Conditional Limit Theorem”. The Annals of Probability vol. 12, no. 3, pp. 768–793, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Dawson, L. Gorostiza, and A. Wakolbinger, “Shrödinger processes and large deviations”, J. Math. Phvs.. vol 31, no. 10. op. 2385–2388. 1990.

    Article  MathSciNet  MATH  Google Scholar 

  7. M.D. Donsker and S.R. Varadhan, “Asymptotic Evaluation of Certain Markov Process Expectations for J arge Time -HI”, Communications on pure and applied Mathematics vol. XXIX, pp. 389–461, 1976.

    Article  MathSciNet  Google Scholar 

  8. E.B. Dynkin, Theorie des Processus Markoviens Dunod: Paris, 1963.

    Google Scholar 

  9. E.B. Dynldn, Markov Processes Volume I, Springer-Verlag: Berlin, Heidelberg, 1965.

    Google Scholar 

  10. E.B. Dynkin, Markov Processes Volume II, Springer-Verlag: Berlin, Heidelberg, 1965.

    MATH  Google Scholar 

  11. W. H. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control Springer-Verlag: Berlin, 1975.

    Book  MATH  Google Scholar 

  12. H. Föllmer, “Random fields and diffusion processes”, in Ecole d’été de Saint Flour XV-XVII (1985–1987) Lecture Notes in Mathematics 1362, Springer-Verlag: Berlin, 1988.

    Google Scholar 

  13. B. Jamison, “Reciprocal Processes”, Z Wahrscheinlichkeitstheorie ver. Gebiete vol. 30, 65, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  14. R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes I, General Theory Springer-Verlag: Berlin Heidelberg, 1977.

    MATH  Google Scholar 

  15. M. Pavon and A. Wakolbinger, “On Free Energy, Stochastic Control, and Schrödinger Processes”, in Proceedings Workshop on Modeling and Control of Uncertain Systems, Birkhäuser, Boston, May 1991.

    Google Scholar 

  16. E. Schrödinger, Sitzungsbericht der Preubischen Akademie, Phys. Math. Classe, 144, 1931.

    Google Scholar 

  17. E. Schrödinger, “Une analogie entre la mécanique ondulatoire et quelques problèmes de probabilités en physique classique”, Annales de l’Institut Henri Poincaré, 11 300, 1932.

    Google Scholar 

  18. D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, Berlin Heidelberg, 1979

    MATH  Google Scholar 

  19. A. Wakolbinger, “A Simplified Variational Characterisation of Schrödinger Processes”,.I. Math. Phys. 30. 2943, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Wakolbinger, “Schrödinger Bridges from 1931 to 1991”, in: E. Cabana et al. (eds) Proc. of the 4th Latin American Congress in Probability and Mathematical Statistics Mexico City 1990, Contribuciones en probabilidad y estadistica matematica 3, pp. 61–79, 1992.

    Google Scholar 

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Blaquière, A., Sigal-Pauchard, M. (1994). Entropy Minimization Problems with Linear Constraints, Schrödinger Bridge and a Conditional Sanov Theorem. In: Guttalu, R.S. (eds) Mechanics and Control. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2425-0_4

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  • DOI: https://doi.org/10.1007/978-1-4615-2425-0_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6029-2

  • Online ISBN: 978-1-4615-2425-0

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