Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

A characterization of reciprocal processes via an integration by parts formula on the path space

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Code(s) de Classification MSC:

Résumé: We characterize in this paper each class of reciprocal processes associated to a Brownian diffusion (therefore not necessarly Gaussian) as the set of Probability measures under which a certain integration by parts formula holds on the path space $\C ([0,1];\R)$. This functional equation can be interpreted as a perturbed duality equation between Malliavin derivative operator and stochastic integration. An application to periodic Ornstein-Uhlenbeck process is presented. We also deduce from our integration by parts formula the existence of Nelson derivatives for general reciprocal processes.

Mots Clés: Reciprocal process ; integration by parts formula ; stochastic bridge ; stochastic differential equation with boundary conditions ; stochastic Newton equation

Date: 2000-10-09

Prépublication numéro: PMA-615