WIAS Preprint No. 796, (2002)

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



Authors

  • Rœlly, Sylvie
  • Thieullen, Michèle

2010 Mathematics Subject Classification

  • 60G15 60G60 60H10 60J60

Keywords

  • reciprocal processes, stochastic bridge, mixture of bridges, integration by parts formula, Malliavin calculus, entropy, time reversal, reversible process

DOI

10.20347/WIAS.PREPRINT.796

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 C([0; 1]; ℝd ). Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov

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