Reciprocal processes. A measure-theoretical point of view

By Christian Léonard, S. Roelly, J. Zambrini. 2013

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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.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a77c7cdddeced114061b0baea107a4e99d0deed2