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
收藏
页码:1 / 31
页数:32
相关论文
共 34 条
[1]  
Allouba Hassan, Different types of spdes in the eyes of girsanov’s theorem, Stochastic analysis and applications, 16, 5, pp. 787-810, (1998)
[2]  
Anderson Theodore W, The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proceedings of the American Mathematical Society, 6, 2, pp. 170-176, (1955)
[3]  
Athreya Siva, Joseph Mathew, Mueller Carl, Small ball probabilities and a support theorem for the stochastic heat equation, The Annals of Probability, 49, 5, pp. 2548-2572, (2021)
[4]  
Balan Raluca M, Conus Daniel, A note on intermittency for the fractional heat equation, Statistics & Probability Letters, 95, pp. 6-14, (2014)
[5]  
Bass Richard F, Probability estimates for multiparameter brownian processes, The Annals of Probability, pp. 251-264, (1988)
[6]  
Bezdek Pavel, On weak convergence of stochastic heat equation with colored noise, Stochastic Processes and their Applications, 126, 9, pp. 2860-2875, (2016)
[7]  
Bogdan Krzysztof, Jakubowski Tomasz, Estimates of heat kernel of fractional laplacian perturbed by gradient operators, Communications in mathematical physics, 271, 1, pp. 179-198, (2007)
[8]  
Brosamler GA, Laws of the iterated logarithm for brownian motions on compact manifolds, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 65, 1, pp. 99-114, (1983)
[9]  
Chen Jiaming, Small ball probabilities for the stochastic heat equation with colored noise, Stochastic Processes and their Applications, 177, (2024)
[10]  
Chen Le, Ouyang Cheng, Vickery William, Parabolic anderson model with colored noise on torus, (2023)