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Pré-Publication, Document De Travail Année : 2014

Reciprocal processes. A measure-theoretical point of view

Christian Léonard
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Sylvie Roelly
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Jean-Claude Zambrini
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Résumé

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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Dates et versions

hal-00850106 , version 1 (02-08-2013)
hal-00850106 , version 2 (15-09-2014)

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Christian Léonard, Sylvie Roelly, Jean-Claude Zambrini. Reciprocal processes. A measure-theoretical point of view. 2014. ⟨hal-00850106v1⟩
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