WIAS Preprint No. 796, (2002)

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



Authors

  • Rœlly, Sylvie
  • Thieullen, Michele

2010 Mathematics Subject Classification

  • 60G15 60G60 60H10 60J60

Keywords

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

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 ( IBPF for short) on the space of continuous paths from [0,1] with values in 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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