On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients

被引：49

作者：

Mytnik, Leonid ^{[1
]}

Perkins, Edwin

Sturm, Anja

机构：

[1] Technion Israel Inst Technol, Fac Ind Engn & Management, IL-32000 Haifa, Israel

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

ANNALS OF PROBABILITY | 2006年 / 34卷 / 05期

关键词：

heat equation; colored noise; stochastic partial differential equation; uniqueness; existence;

D O I：

10.1214/009117906000000331

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 consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on R-d for d >= 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Holder continuity of the solutions near zero is established.

引用

页码：1910 / 1959

页数：50

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