STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION
文献类型：期刊论文
| 作者 | Chen, Chuchu; Hong, Jialin ; Lu, Yulan2
|
| 刊名 | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
 |
| 出版日期 | 2022-06-01 |
| 页码 | 43 |
| 关键词 | Invariant measure Markov chain weak convergence backward Euler method stochastic differential equations with piecewise continuous arguments |
| ISSN号 | 1531-3492 |
| DOI | 10.3934/dcdsb.2022098 |
| 英文摘要 | For the stochastic differential equation with piecewise continuous arguments, multiplicative noises and dissipative drift coefficients, we show that the solution at integer time is a Markov chain and admits a unique invariant measure. In order to numerically preserve the invariant measure, we apply the backward Euler method to the equation, and prove that the numerical solution at integer time is also a Markov chain and possesses a unique numerical invariant measure. By establishing several a priori estimations, we present the time-independent weak error analysis for the method via Malliavin calculus, which implies that the numerical invariant measure converges to the original one with weak order 1. Numerical experiments verify the theoretical analysis. |
| 资助项目 | National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[11871068] ; National Natural Science Foundation of China[12031020] ; National Natural Science Foundation of China[12022118] ; National Natural Science Foundation of China[12026428] ; Youth Innovation Promotion Association CAS ; National Postdoctoral Program for Innovative Talents[BX20180347] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000809595000001 |
| 出版者 | AMER INST MATHEMATICAL SCIENCES-AIMS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/61532]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Lu, Yulan |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Chen, Chuchu,Hong, Jialin,Lu, Yulan. STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2022:43. |
| APA | Chen, Chuchu,Hong, Jialin,&Lu, Yulan.(2022).STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,43. |
| MLA | Chen, Chuchu,et al."STOCHASTIC DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS: MARKOV PROPERTY, INVARIANT MEASURE AND NUMERICAL APPROXIMATION".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2022):43. |
入库方式： OAI收割
来源：数学与系统科学研究院
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