Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on S2

被引：4
作者：
Lan, Xiaohong [1 ]
Xiao, Yimin [2 ]
机构：
[1] Univ Sci & Technol China, Sch Math Sci, Hefei, Anhui, Peoples R China
[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 476卷 / 01期
基金：
美国国家科学基金会;
关键词：
Stochastic heat equation; Fractional-colored Gaussian noise; Spherical random fields; Strong local nondeterminism; Uniform modulus of continuity; CONTINUITY; CIRCLE;
D O I：
10.1016/j.jmaa.2019.01.077
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the linear stochastic heat equation driven by an additive infinite dimensional fractional Brownian noise on the unit sphere S-2. The existence and uniqueness of its solution in certain Sobolev space is investigated and sample path regularity properties are established. In particular, the exact uniform modulus of continuity of the solution in time/spatial variable is derived. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：27 / 52
页数：26
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