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Reciprocal processes. A measure-theoretical point of view

Abstract : This is a survey paper about reciprocal processes. The bridges of a Markov process are also Markov. But an arbitrary mixture of these bridges fails to be Markov in general. However, it still enjoys the interesting properties of a reciprocal process. The structures of Markov and reciprocal processes are recalled with emphasis on their time-symmetries. A review of the main properties of the reciprocal processes is presented. Our measure-theoretical approach allows for a unified treatment of the diffusion and jump processes. Abstract results are illustrated by several examples and counter-examples.
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https://hal.archives-ouvertes.fr/hal-00850106
Contributor : Christian Léonard <>
Submitted on : Monday, September 15, 2014 - 6:49:22 PM
Last modification on : Tuesday, March 2, 2021 - 10:14:25 AM
Long-term archiving on: : Tuesday, December 16, 2014 - 11:42:04 AM

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  • HAL Id : hal-00850106, version 2
  • ARXIV : 1308.0576

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Christian Léonard, Sylvie Roelly, Jean-Claude Zambrini. Reciprocal processes. A measure-theoretical point of view. Probability Surveys, Institute of Mathematical Statistics (IMS), 2014, pp.237-269. ⟨hal-00850106v2⟩

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