Stochastic PDEs Driven by Nonlinear Noise and Backward Doubly SDEs

Anis Matoussi () and Michael Scheutzow ()
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Anis Matoussi: Technische Universität Berlin

Journal of Theoretical Probability, 2002, vol. 15, issue 1, 1-39

Abstract: Abstract We study a “new kind” of backward doubly stochastic differential equations, where the nonlinear noise term is given by Itô–Kunita's stochastic integral. This allows us to give a probabilistic interpretation of classical and Sobolev's solutions of semilinear parabolic stochastic partial differential equations driven by a nonlinear space-time noise.

Keywords: stochastic partial differential equation; Backward SDE; Feynman–Kac's formula; Itô–Kunita's stochastic integral; stochastic flow (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1013803104760

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