A PDE approach to large deviations in Hilbert spaces

Swie[combining cedilla]ch, Andrzej

Stochastic Processes and their Applications, 2009, vol. 119, issue 4, 1081-1123

Abstract: We introduce a PDE approach to the large deviation principle for Hilbert space valued diffusions. It can be applied to a large class of solutions of abstract stochastic evolution equations with small noise intensities and is adaptable to some special equations, for instance to the 2D stochastic Navier-Stokes equations. Our approach uses a lot of ideas from (and in significant part follows) the program recently developed by Feng and Kurtz [J. Feng, T. Kurtz, Large Deviations for Stochastic Processes, in: Mathematical Surveys and Monographs, vol. 131, American Mathematical Society, Providence, RI, 2006]. Moreover we present easy proofs of exponential moment estimates for solutions of stochastic PDE.

Keywords: Large; deviations; Viscosity; solutions; Hamilton-Jacobi-Bellman; equations; Stochastic; PDE; Stochastic; Navier-Stokes; equations (search for similar items in EconPapers)
Date: 2009
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