Probability Surveys

Reciprocal processes. A measure-theoretical point of view

Christian Léonard, Sylvie Rœlly, and Jean-Claude Zambrini

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Abstract

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.

Article information

Source
Probab. Surveys, Volume 11 (2014), 237-269.

Dates
First available in Project Euclid: 10 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ps/1412947842

Digital Object Identifier
doi:10.1214/13-PS220

Mathematical Reviews number (MathSciNet)
MR3269228

Zentralblatt MATH identifier
1317.60004

Keywords
Markov process reciprocal process Markov bridge time-symmetry entropy minimization

Citation

Léonard, Christian; Rœlly, Sylvie; Zambrini, Jean-Claude. Reciprocal processes. A measure-theoretical point of view. Probab. Surveys 11 (2014), 237--269. doi:10.1214/13-PS220. https://projecteuclid.org/euclid.ps/1412947842


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