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Large Deviations Principles for Symplectic Discretizations of Stochastic Linear Schrodinger Equation
Chen, Chuchu1,2; Hong, Jialin1,2; Jin, Diancong1,2,3,4; Sun, Liying1,2
2022-03-29
Source PublicationPOTENTIAL ANALYSIS
ISSN0926-2601
Pages41
AbstractIn 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.
KeywordLarge deviations principle Symplectic discretizations Stochastic Schrodinger equation Rate function Exponential tightness
DOI10.1007/s11118-022-09990-z
Indexed BySCI
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000774717000001
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/60246
Collection中国科学院数学与系统科学研究院
Corresponding AuthorJin, Diancong
Affiliation1.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
Recommended Citation
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.
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