KMS Of Academy of mathematics and systems sciences, CAS
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 Publication | POTENTIAL ANALYSIS |
ISSN | 0926-2601 |
Pages | 41 |
Abstract | 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. |
Keyword | Large deviations principle Symplectic discretizations Stochastic Schrodinger equation Rate function Exponential tightness |
DOI | 10.1007/s11118-022-09990-z |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000774717000001 |
Publisher | SPRINGER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60246 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Jin, Diancong |
Affiliation | 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 |
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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