Stochastic flows and Bismut formulas for stochastic Hamiltonian systems

Xicheng Zhang

Stochastic Processes and their Applications, 2010, vol. 120, issue 10, 1929-1949

Abstract: We first consider the stochastic differential equations (SDE) without global Lipschitz conditions, and give sufficient conditions for the SDEs to be strictly conservative. In particular, a criteria for stochastic flows of diffeomorphisms defined by SDEs with non-global Lipschitz coefficients is obtained. We also use Zvonkin's transformation to derive a stochastic flow of C1-diffeomorphisms for non-degenerate SDEs with Hölder continuous drifts. Next, we prove a Bismut type formula for certain degenerate SDEs. Lastly, we apply our results to stochastic Hamiltonian systems, which in particular covers the following stochastic nonlinear oscillator equation where has a bounded first order derivative, and is a one dimensional Brownian white noise.

Keywords: Stochastic flow of diffeomorphisms Bismut formula; Stochastic Hamiltonian system (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (9)

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