Stochastic Differential Equations: A Wiener Chaos Approach

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A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of ordinary and partial differential equations driven by finite- or infinite-dimensional noise with either adapted or anticipating input. Existence, uniqueness, regularity, and probabilistic representation of this Wiener Chaos solution is established for a large class of equations. A number of examples are presented to illustrate the general constructions. A detailed analysis is presented for the various forms of the passive scalar equation and for the first-order Itô stochastic partial differential equation. Applications to nonlinear filtering if diffusion processes and to the stochastic Navier-Stokes equation are also discussed.

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Probability, 60H15

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http://salesiana.dossiersoluciones.com/handle/123456789/75022

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504559
 http://arxiv.org/abs/math/0504559

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arXiv