A UNIFIED APPROACH TO STOCHASTIC EVOLUTION EQUATIONS USING THE SKOROKHOD INTEGRAL

被引：2

作者：

Lototsky, S. V. ^{[1
]}

Rozovskii, B. L. ^{[2
]}

机构：

[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2010年 / 54卷 / 02期

基金：

美国国家科学基金会;

关键词：

generalized random elements; Malliavin calculus; Wick product; Wiener chaos; weighted spaces;

D O I：

10.1137/S0040585X97984152

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study stochastic evolution equations driven by Gaussian noise. The key features of the model are that the operators in the deterministic and stochastic parts can have the same order and that the noise can be time-only, space-only, or space-time. Even the simplest equations of this kind do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition leads to natural weights and a natural replacement of the square integrability condition.

引用

页码：189 / 202

页数：14

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