STOCHASTIC HEAT EQUATION WITH ROUGH DEPENDENCE IN SPACE

被引：40

作者：

Hu, Yaozhong ^{[1
]}

Huang, Jingyu ^{[1
]}

Le, Khoa ^{[1
]}

Nualart, David ^{[1
]}

Tindel, Samy ^{[2
]}

机构：

[1] Univ Kansas, Dept Math, 405 Snow Hall, Lawrence, KS 66045 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

ANNALS OF PROBABILITY | 2017年 / 45卷 / 6B期

基金：

美国国家科学基金会;

关键词：

Stochastic heat equation; fractional Brownian motion; Feynman-Kac formula; Wiener chaos expansion; intermittency; EXISTENCE;

D O I：

10.1214/16-AOP1172

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：

This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H is an element of (1/4, 1/2) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient sigma(u) is differentiable with a Lipschitz derivative and sigma(0) = 0.

引用

页码：4561 / 4616

页数：56

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