• S. ROELLY
• M. THIEULLEN

Code(s) de Classification MSC:

• 60G15 Gaussian processes
• 60G60 Random fields
• 60H10 Stochastic ordinary differential equations, See Also {
• 60J60 Diffusion processes, See also {58G32}

Résumé: In this paper we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths $C([0;1];{\R}^d)$. Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov.

Mots Clés: reciprocal processes ; stochastic bridge ; mixture of bridges ; integration by parts formula ; Malliavin calculus ; entropy ; time reversal ; reversible process

Date: 2002-12-20

Prépublication numéro: PMA-784