Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

被引：5

作者：

Chakraborty, Prakash ^{[1
]}

Chen, Xia ^{[2
]}

Gao, Bo ^{[2
]}

Tindel, Samy ^{[3
]}

机构：

[1] Purdue Univ, Dept Stat, 150 N Univ St, W Lafayette, IN 47907 USA

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[3] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2020年 / 130卷 / 11期

关键词：

Stochastic heat equation; Parabolic Anderson model; Fractional Brownian motion; Feynman-Kac formula; Lyapounov exponent; BROWNIAN-MOTION;

D O I：

10.1016/j.spa.2020.06.007

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：

In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise (W)over dot in space. We consider the case H < 1/2 and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman-Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form 1/2 Delta + (W)over dot. (C) 2020 Elsevier B.V. All rights reserved.

引用

页码：6689 / 6732

页数：44

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