Abstract
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.
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Received: 25 October 2000 / Revised version: 7 September 2001 / Published online: 13 May 2002
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Rœlly, S., Thieullen, M. A characterization of reciprocal processes via an integration by parts formula on the path space. Probab Theory Relat Fields 123, 97–120 (2002). https://doi.org/10.1007/s004400100184
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DOI: https://doi.org/10.1007/s004400100184
Keywords
- Path Space
- Part Formula
- Reciprocal Process