空间非齐次白噪声驱动的分数阶随机热方程的矩估计  

Moment Bounds for the Fractional Stochastic Heat Equation with Spatially Inhomogeneous White Noise

作　　者：刘俊峰[1] 毛磊 王志[3] Liu Junfeng;Mao Lei;Wang Zhi(School of Statistics and Data Science,Nanjing Audit University,Nanjing,211815;Department of General Education,Army Engineering University of PLA,Nanjing 211100;School of Sciences,Ningbo University of Technology,Zhejiang Ningbo 315211)

机构地区：[1]南京审计大学统计与数据科学学院,南京211815 [2]陆军工程大学基础部,南京211100 [3]宁波工程学院理学院,浙江宁波315211

出　　处：《数学物理学报（A辑）》2022年第4期1186-1208,共23页Acta Mathematica Scientia

基　　金：国家自然科学基金(11701304);教育部人文社会科学基金(18YJCZH101);江苏高校自然科学基金重大项目(18KJA110002);宁波市自然科学基金(2019A610041);王宽诚教育基金会。

摘　　要：该文主要研究如下伴有Cauchy初值条件的分数阶随机热方程■其中a∈(1,2]为算子D_(δ)^(α)的阶数,δ(|δ|≤2-α)称为偏度参数,扩散系数g(·):R→R是非随机的可测函数:?^(2)/?_(t)?_(x)w_(ρ)(t,x)表示空间非齐次白噪声,在关于非齐次布朗单w_(ρ)(t,x)催化测度ρ的适当假设下,证明了该方程解的存在性、唯一性和H?lder连续性.同时,也证明了方程解的矩估计.In this paper,we will study a class of fractional stochastic heat equation of the form■,00,where D_(δ)^(α)denotes a nonlocal fractional differential operator withα∈(1,2]and|δ|≤2-α,and?~2/?_(t)?_(x)w_(ρ)(t,x)is a spatially inhomogeneous white noise.Under some mild assumptions on the catalytic measure of the inhomogeneous Brownian sheet w_(ρ)(t,x),we prove the existence,uniqueness and Holder regularity of the solution.Upper and lower moment bounds for the solution are also derived.

关 键 词：分数阶随机热方程 空间非齐次白噪声 H?lder连续性 矩估计 

分 类 号：O211.63[理学—概率论与数理统计]