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1 MODAL-X - Modélisation aléatoire de Paris X 2 Institut für Mathematik Potsdam 3 GFMUL - Grupo de Fisica Matematica

Abstract : 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.

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





Author: Christian Léonard - Sylvie Roelly - Jean-Claude Zambrini -

Source: https://hal.archives-ouvertes.fr/



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