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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**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:** 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*