Open Access
2014 Reciprocal processes. A measure-theoretical point of view
Christian Léonard, Sylvie Rœlly, Jean-Claude Zambrini
Probab. Surveys 11: 237-269 (2014). DOI: 10.1214/13-PS220


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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Christian Léonard. Sylvie Rœlly. Jean-Claude Zambrini. "Reciprocal processes. A measure-theoretical point of view." Probab. Surveys 11 237 - 269, 2014.


Published: 2014
First available in Project Euclid: 10 October 2014

zbMATH: 1317.60004
MathSciNet: MR3269228
Digital Object Identifier: 10.1214/13-PS220

Keywords: Entropy minimization , Markov bridge , Markov process , reciprocal process , time-symmetry

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.11 • 2014
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