Holder continuity for stochastic fractional heat equation with colored noise

被引：6
作者：
Li, Kexue [1 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
来源：
STATISTICS & PROBABILITY LETTERS | 2017年 / 129卷
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Stochastic fractional heat equation; Fractional heat kernel; Colored noise; Holder continuity; PARTIAL-DIFFERENTIAL-EQUATIONS; KERNEL; LAPLACIAN;
D O I：
10.1016/j.spl.2017.04.020
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 paper, we consider semilinear stochastic fractional heat equation partial derivative u(t)/partial derivative t = - (-Delta)(beta/2)u(t) + sigma(u(t))(eta) over dot. The Gaussian noise (eta) over dot is assumed to be colored in space with covariance of the form E((eta) over dot(t, x)(eta) over dot(s, y)) = delta(0)(t - s)f(alpha)(x - y), where f(alpha) is the Riesz kernel f(alpha)(x) alpha vertical bar x vertical bar(-alpha). We obtain the spatial and temporal Holder continuity of the mild solution. (C) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码：34 / 41
页数：8
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