Reciprocal processes. A measure-theoretical point of view

Christian Léonard (1) , Sylvie Roelly (2) , Jean-Claude Zambrini (3)

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

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.

Mots clés: Markov process; reciprocal process; time symmetry; Markov bridge; entropy minimization

Domaines: Probabilités [math.PR]

Christian Léonard, Sylvie Roelly, Jean-Claude Zambrini. Reciprocal processes. A measure-theoretical point of view. Probability Surveys, 2014, 11, pp.237-269. ⟨hal-00850106v2⟩