Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density

doi:10.1093/imanum/drac011

CSpace

	Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density
	Chen, Chuchu 1,2; Cui, Jianbo 3; Hong, Jialin 1,2; Sheng, Derui 1,2
	2022-04-19
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
页码	40
摘要	This paper studies the numerical approximation of the density of the stochastic heat equation driven by space-time white noise via the accelerated exponential Euler scheme. The existence and smoothness of the density of the numerical solution are proved by means of Malliavin calculus. Based on a priori estimates of the numerical solution we present a test-function-independent weak convergence analysis, which is crucial to show the convergence of the density. The convergence order of the density in uniform convergence topology is shown to be exactly 1/2 in the nonlinear drift case and nearly 1 in the affine drift case. As far as we know, this is the first result on the existence and convergence of density of the numerical solution to the stochastic partial differential equation.
关键词	density convergence order accelerated exponential Euler scheme stochastic heat equation Malliavin calculus
DOI	10.1093/imanum/drac011
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[11871068] ; National Natural Science Foundation of China[12031020] ; National Natural Science Foundation of China[12022118] ; Youth Innovation Promotion Association CAS ; Hong Kong Polytechnic University[P0039016] ; CAS AMSS-PolyU Joint Laboratory of Applied Mathematics
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000786107500001
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60320
专题	中国科学院数学与系统科学研究院
通讯作者	Sheng, Derui
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong 999077, Peoples R China
推荐引用方式 GB/T 7714	Chen, Chuchu,Cui, Jianbo,Hong, Jialin,et al. Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2022:40.
APA	Chen, Chuchu,Cui, Jianbo,Hong, Jialin,&Sheng, Derui.(2022).Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density.IMA JOURNAL OF NUMERICAL ANALYSIS,40.
MLA	Chen, Chuchu,et al."Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density".IMA JOURNAL OF NUMERICAL ANALYSIS (2022):40.