Minimization of the Kullback information for some Markov processes

  • P. Cattiaux
  • C. Léonard
Part of the Lecture Notes in Mathematics book series (LNM, volume 1626)


We extend previous results of the authors ([CaL1] and [Cal2]) to general Markov processes which admit a “carré du champ” operator. This yields variational characterizations for the existence of Markov processes with a given flow of time marginal laws which is the stochastic quantization problem, extending previous results obtained by P.A. Meyer and W.A. Zheng or S. Albeverio and M. Röckner in the symmetric case to nonsymmetric processes.


Markov Process Relative Entropy Polish Space Dirichlet Form Large Deviation Principle 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • P. Cattiaux
    • 1
    • 5
    • 2
  • C. Léonard
    • 3
    • 5
    • 4
  1. 1.Ecole PolytechniqueCMAPPalaiseau CedexFrance
  2. 2.URA CNRS 756France
  3. 3.Equipe de Modélisation Stochastique et StatistiqueUniversité de Paris-SudOrsay CedexFrance
  4. 4.URA CNRS 743France
  5. 5.Equipe ModalXUniversité de Paris XNanterre CedexFrance

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