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A characterization of reciprocal processes via an integration by parts formula on the path space
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  • Published: May 2002

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

  • Sylvie Rœlly1 &
  • Michèle Thieullen2 

Probability Theory and Related Fields volume 123, pages 97–120 (2002)Cite this article

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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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Authors and Affiliations

  1. Centre de Mathématiques Appliquées, UMR CNRS 7641, École Polytechnique, 91128 Palaiseau Cédex, France. e-mail: roelly@cmapx.polytechnique.fr, , , , , , FR

    Sylvie Rœlly

  2. Laboratoire de Probabilités et Modèles Aléatoires, UMR CNRS 7599, Université Paris 6, boite 188, 4, place Jussieu, 75252 Paris Cédex 05, France. e-mail: mth@ccr.jussieu.fr, , , , , , FR

    Michèle Thieullen

Authors
  1. Sylvie Rœlly
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  2. Michèle Thieullen
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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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  • Issue Date: May 2002

  • DOI: https://doi.org/10.1007/s004400100184

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Keywords

  • Path Space
  • Part Formula
  • Reciprocal Process
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