Abstract
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.
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Cattiaux, P., Léonard, C. (1996). Minimization of the Kullback information for some Markov processes. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXX. Lecture Notes in Mathematics, vol 1626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094655
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DOI: https://doi.org/10.1007/BFb0094655
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