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

We characterize in this paper the class of reciprocal processes associated to a Brownian diffusion (therefore not necessarily Gaussian) as the set of Probability measures under which a certain integration by parts formula holds on the path space . This functional equation can be interpreted as a per...

Full description

Saved in:
Bibliographic Details
Published in:Probability theory and related fields 2002-05, Vol.123 (1), p.97-120
Main Authors: ROELLY, Sylvie, THIEULLEN, Michèle
Format: Article
Language:English
Subjects:
Exact sciences and technology
Formulas (mathematics)
Functional equations
Markov processes
Mathematics
Operators (mathematics)
Ornstein-Uhlenbeck process
Probability
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic analysis
Stochastic processes
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We characterize in this paper the class of reciprocal processes associated to a Brownian diffusion (therefore not necessarily Gaussian) as the set of Probability measures under which a certain integration by parts formula holds on the path space . 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.
ISSN:0178-8051
1432-2064
DOI:10.1007/s004400100184