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.
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页码：1910 / 1959
页数：50
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