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 Probability Surveys > Vol. 11 (2014) open journal systems 


Reciprocal processes. A measure-theoretical point of view

Christian Léonard, Paris Ouest University
Sylvie Rœlly, Potsdam University
Jean-Claude Zambrini, GFM, Lisbon University


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.

Keywords: Markov process, reciprocal process, Markov bridge, time-symmetry, entropy minimization.

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

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