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ASYMPTOTICALLY-PRESERVING LARGE DEVIATIONS PRINCIPLES BY STOCHASTIC SYMPLECTIC METHODS FOR A LINEAR STOCHASTIC OSCILLATOR

文献类型：期刊论文

作者Chen, Chuchu1,2; Hong, Jialing1,2; Jin, Diancong1,2; Sun, Liying1,2
刊名SIAM JOURNAL ON NUMERICAL ANALYSIS
出版日期2021
卷号59期号:1页码:32-59
关键词stochastic symplectic methods superiority large deviations principle rate function asymptotical preservation
ISSN号0036-1429
DOI10.1137/19M1306919
英文摘要It is well known that symplectic methods have been rigorously shown to be superior to nonsymplectic ones especially in long-time computation, when applied to deterministic Hamiltonian systems. In this paper, we attempt to study the superiority of stochastic symplectic methods by means of the large deviations principle. We propose the concept of asymptotical preservation of numerical methods for large deviations principles associated with the exact solutions of the general stochastic Hamiltonian systems. Considering that the linear stochastic oscillator is one of the typical stochastic Hamiltonian systems, we take it as the test equation in this paper to obtain precise results about the rate functions of large deviations principles for both exact and numerical solutions. Based on the Gartner-Ellis theorem, we first study the large deviations principles of the mean position and the mean velocity for both the exact solution and its numerical approximations. Then, we prove that stochastic symplectic methods asymptotically preserve these two large deviations principles, but nonsymplectic ones do not. This indicates that stochastic symplectic methods are able to approximate well the exponential decay speed of the "hitting probability" of the mean position and mean velocity of the stochastic oscillator. Finally, numerical experiments are performed to show the superiority of stochastic symplectic methods in computing the large deviations rate functions. To the best of our knowledge, this is the first result about applying the large deviations principle to reveal the superiority of stochastic symplectic methods compared with nonsymplectic ones in the existing literature.
资助项目National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[11711530071] ; National Natural Science Foundation of China[11871068] ; National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[12031020] ; National Natural Science Foundation of China[12022118]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000625044600002
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58266]  
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, 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, Jialing,Jin, Diancong,et al. ASYMPTOTICALLY-PRESERVING LARGE DEVIATIONS PRINCIPLES BY STOCHASTIC SYMPLECTIC METHODS FOR A LINEAR STOCHASTIC OSCILLATOR[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2021,59(1):32-59.
APA Chen, Chuchu,Hong, Jialing,Jin, Diancong,&Sun, Liying.(2021).ASYMPTOTICALLY-PRESERVING LARGE DEVIATIONS PRINCIPLES BY STOCHASTIC SYMPLECTIC METHODS FOR A LINEAR STOCHASTIC OSCILLATOR.SIAM JOURNAL ON NUMERICAL ANALYSIS,59(1),32-59.
MLA Chen, Chuchu,et al."ASYMPTOTICALLY-PRESERVING LARGE DEVIATIONS PRINCIPLES BY STOCHASTIC SYMPLECTIC METHODS FOR A LINEAR STOCHASTIC OSCILLATOR".SIAM JOURNAL ON NUMERICAL ANALYSIS 59.1(2021):32-59.

入库方式： OAI收割

来源：数学与系统科学研究院

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