Stochastic differential equations: A Wiener chaos approach

被引:43
|
作者
Lototsky, S [1 ]
Rozovskii, B [1 ]
机构
[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA
关键词
anticipating equations; generalized random elements; degenerate parabolic equations; Malliavin calculus; passive scalar equation; Skorohod integral; S-transform; weighted spaces;
D O I
10.1007/978-3-540-30788-4_23
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
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 Ito stochastic partial differential equation. Applications to nonlinear filtering of diffusion processes and to the stochastic Navier-Stokes equation are also discussed.
引用
收藏
页码:433 / +
页数:4
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