Large Deviations Principles for Symplectic Discretizations of Stochastic Linear Schrodinger Equation

doi:10.1007/s11118-022-09990-z

CSpace

	Large Deviations Principles for Symplectic Discretizations of Stochastic Linear Schrodinger Equation
	Chen, Chuchu 1,2; Hong, Jialin 1,2; Jin, Diancong 1,2,3,4; Sun, Liying 1,2
	2022-03-29
发表期刊	POTENTIAL ANALYSIS
ISSN	0926-2601
页码	41
摘要	In this paper, we consider the large deviations principles (LDPs) for the stochastic linear Schrodinger equation and its symplectic discretizations. These numerical discretizations are the spatial semi-discretization based on the spectral Galerkin method, and the further full discretizations with symplectic schemes in temporal direction. First, by means of the abstract Gartner-Ellis theorem, we prove that the observable B-T = u(T)/T, T > 0 of the exact solution u is exponentially tight and satisfies an LDP on L-2(0, pi; C). Then, we present the LDPs for both {B-T(M)}(T>0 )of the spatial discretization {u(M)}(M is an element of N) and {B-N(M)}(N is an element of N) of the full disum cretization {u(N)(M)}(M,N is an element of N), where B-T(M) = u(M)(T)/T and B-N(M) = u(N)(M)/N-tau are the discrete approximations of B-T. Further, we show that both the semi-discretization {u(M)}(M is an element of N) and the full discretization {u(N)(M)}(M,N is an element of N) based on temporal symplectic schemes can weakly asymptotically preserve the LDP of {B-T}(T>0). These results show the ability of symplectic discretizations to preserve the LDP of the stochastic linear Schrodinger equation, and first provide an effective approach to approximating the large deviations rate function in infinite dimensional space based on the numerical discretizations.
关键词	Large deviations principle Symplectic discretizations Stochastic Schrodinger equation Rate function Exponential tightness
DOI	10.1007/s11118-022-09990-z
收录类别	SCI
语种	英语
资助项目	National key R&D Program of China[2020YFA0713701] ; National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[11871068] ; National Natural Science Foundation of China[12026428] ; National Natural Science Foundation of China[12031020] ; National Natural Science Foundation of China[12022118] ; National Natural Science Foundation of China[12101596] ; National Natural Science Foundation of China[12171047] ; Youth Innovation Promotion Association CAS ; China Postdoctoral Science Foundation[BX2021345] ; China Postdoctoral Science Foundation[2021M690163] ; Fundamental Research Funds for the Central Universities[3004011142]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000774717000001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60246
专题	中国科学院数学与系统科学研究院
通讯作者	Jin, Diancong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China 4.Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
推荐引用方式 GB/T 7714	Chen, Chuchu,Hong, Jialin,Jin, Diancong,et al. Large Deviations Principles for Symplectic Discretizations of Stochastic Linear Schrodinger Equation[J]. POTENTIAL ANALYSIS,2022:41.
APA	Chen, Chuchu,Hong, Jialin,Jin, Diancong,&Sun, Liying.(2022).Large Deviations Principles for Symplectic Discretizations of Stochastic Linear Schrodinger Equation.POTENTIAL ANALYSIS,41.
MLA	Chen, Chuchu,et al."Large Deviations Principles for Symplectic Discretizations of Stochastic Linear Schrodinger Equation".POTENTIAL ANALYSIS (2022):41.