On a stochastic partial differential equation with a fractional Laplacian operator

被引：21
|
作者：
Chang, Tongkeun [1 ]
Lee, Kijung [2 ]
机构：
[1] Yonsei Univ, Dept Math, Seoul 120749, South Korea
[2] Ajou Univ, Dept Math, Suwon 443749, South Korea
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 09期
基金：
新加坡国家研究基金会;
关键词：
Stochastic partial differential equations; Fractional Laplacian operators; Regularity;
D O I：
10.1016/j.spa.2012.04.015
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 article, we consider the regularity of the solution of du(t, x) = (Delta alpha/2 u (t, x) + f (t, x))dt + Sigma(m)(i=1) g(i) (t, x)dw(t)(i), u(0, x) = u(0)(x). We adopt the framework given in some works of Krylov which are related to the theory of stochastic partial differential equations with the Laplace operator. We construct the important estimates for the theory and prove regularity theorems using them. (c) 2012 Elsevier B.V. All rights reserved.
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页码：3288 / 3311
页数：24
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