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Duality formula for the bridges of a Brownian diffusion: Application to gradient drifts

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  • Roelly, Sylvie
  • Thieullen, Michèle

Abstract

In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths . Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov.

Suggested Citation

  • Roelly, Sylvie & Thieullen, Michèle, 2005. "Duality formula for the bridges of a Brownian diffusion: Application to gradient drifts," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1677-1700, October.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:10:p:1677-1700
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    Cited by:

    1. Conforti, Giovanni & Léonard, Christian, 2017. "Reciprocal classes of random walks on graphs," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1870-1896.
    2. Giovanni Conforti & Paolo Dai Pra & Sylvie Rœlly, 2017. "Reciprocal Class of Jump Processes," Journal of Theoretical Probability, Springer, vol. 30(2), pages 551-580, June.

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