Small ball probabilities for the fractional stochastic heat equation driven by a colored noise

被引：0

作者：

Chen, Jiaming ^{[1
]}

机构：

[1] Univ Rochester, Dept Math, Rochester, NY 14627 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2025年 / 30卷

关键词：

stochastic heat equation; fractional Laplacian; spatial homogeneous colored noise; small ball probabilities;

D O I：

10.1214/25-EJP1295

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 fractional stochastic heat equation on the d-dimensional torus T-d:=[-1/2,1/2](d), d >= 1, with periodic boundary conditions: partial derivative(t)u(t,x)= -(-Delta)(alpha/2)u(t,x)+sigma(t,x,u)F-center dot(t,x)x is an element of T-d,t is an element of R+, where alpha is an element of (1,2] and F-center dot(t,x) is a generalized Gaussian noise which is white in time and colored in space. Assuming that sigma is Lipschitz in u and uniformly bounded, we estimate small ball probabilities for the solution u when u(0,x)equivalent to 0.

引用

页码：1 / 31

页数：32

共 34 条

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