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

doi:10.1137/19M1306919

CSpace

	ASYMPTOTICALLY-PRESERVING LARGE DEVIATIONS PRINCIPLES BY STOCHASTIC SYMPLECTIC METHODS FOR A LINEAR STOCHASTIC OSCILLATOR
	Chen, Chuchu 1,2; Hong, Jialing 1,2; Jin, Diancong 1,2; Sun, Liying 1,2
	2021
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	59 期号:1 页码:32-59
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.
关键词	stochastic symplectic methods superiority large deviations principle rate function asymptotical preservation
DOI	10.1137/19M1306919
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000625044600002
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58267
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.