Stochastic Differential Equations: A Wiener Chaos Approach
| dc.creator | Lototsky, S. V. | |
| dc.creator | Rozovskii, B. L. | |
| dc.date | 2005-04-27 | |
| dc.date.accessioned | 2026-07-07T05:19:26Z | |
| dc.date.available | 2026-07-07T05:19:26Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0504559 | |
| dc.identifier | http://arxiv.org/abs/math/0504559 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75022 | |
| dc.subject | Probability | |
| dc.subject | 60H15 | |
| dc.title | Stochastic Differential Equations: A Wiener Chaos Approach | |
| dc.type | text |