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
收藏
页码：6689 / 6732
页数：44
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