STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION

doi:10.3934/dcdsb.2022098

	STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION
	Chen, Chuchu ; Hong, Jialin; Lu, Yulan 1
	2022-06-01
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
ISSN	1531-3492
页码	43
摘要	For the stochastic differential equation with piecewise continuous arguments, multiplicative noises and dissipative drift coefficients, we show that the solution at integer time is a Markov chain and admits a unique invariant measure. In order to numerically preserve the invariant measure, we apply the backward Euler method to the equation, and prove that the numerical solution at integer time is also a Markov chain and possesses a unique numerical invariant measure. By establishing several a priori estimations, we present the time-independent weak error analysis for the method via Malliavin calculus, which implies that the numerical invariant measure converges to the original one with weak order 1. Numerical experiments verify the theoretical analysis.
关键词	Invariant measure Markov chain weak convergence backward Euler method stochastic differential equations with piecewise continuous arguments
DOI	10.3934/dcdsb.2022098
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] ; National Natural Science Foundation of China[12026428] ; Youth Innovation Promotion Association CAS ; National Postdoctoral Program for Innovative Talents[BX20180347]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000809595000001
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61533
专题	计算数学与科学工程计算研究所
通讯作者	Lu, Yulan
作者单位	1.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100049, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Chen, Chuchu,Hong, Jialin,Lu, Yulan. STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2022:43.
APA	Chen, Chuchu,Hong, Jialin,&Lu, Yulan.(2022).STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,43.
MLA	Chen, Chuchu,et al."STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2022):43.