STOCHASTIC HEAT EQUATION WITH ROUGH DEPENDENCE IN SPACE

被引：44

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

共 15 条

[11] The Kolmogorov-Riesz compactness theorem [J].

Hanche-Olsen, Harald ;

Holden, Helge .

EXPOSITIONES MATHEMATICAE, 2010, 28 (04) :385-394

[12] Stochastic evolution equations with a spatially homogeneous Wiener process [J].

Peszat, S ;

Zabczyk, J .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1997, 72 (02) :187-204

[13] Integration questions related to fractional Brownian motion [J].

Pipiras, V ;

Taqqu, MS .

PROBABILITY THEORY AND RELATED FIELDS, 2000, 118 (02) :251-291

[14]

Samko A. A., 1993, Fractional Integrals andDerivatives: Theory and Applications

[15] MORREY SPACE [J].

ZORKO, CT .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 98 (04) :586-592

← 1 2 →