Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions
文献类型：期刊论文
| 作者 | Hong, Jialin; Huang, Chuying2; Wang, Xu |
| 刊名 | IMA JOURNAL OF NUMERICAL ANALYSIS
 |
| 出版日期 | 2021-04-01 |
| 卷号 | 41期号:2页码:1608-1638 |
| 关键词 | fractional Brownian motion strong convergence rate Runge-Kutta method simplified step-N Euler scheme |
| ISSN号 | 0272-4979 |
| DOI | 10.1093/imanum/draa019 |
| 英文摘要 | This paper investigates numerical schemes for stochastic differential equations driven by multi-dimensional fractional Brownian motions (fBms) with Hurst parameter H is an element of 1/2, 1). Based on the continuous dependence of numerical solutions on the driving noises, we propose the order conditions of Runge-Kutta methods for the strong convergence rate 2H - 1/2, which is the optimal strong convergence rate for approximating the Levy area of fBms. We provide an alternative way to analyse the convergence rate of explicit schemes by adding 'stage values' such that the schemes are interpreted as Runge-Kutta methods. Taking advantage of this technique the strong convergence rate of simplified step-N Euler schemes is obtained, which gives an answer to a conjecture in Deya et al. (2012) when H is an element of 1/2, 1). Numerical experiments verify the theoretical convergence rate. |
| 资助项目 | National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[11871068] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000651815700026 |
| 出版者 | OXFORD UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/58701]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Huang, Chuying |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Hong, Jialin,Huang, Chuying,Wang, Xu. Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2021,41(2):1608-1638. |
| APA | Hong, Jialin,Huang, Chuying,&Wang, Xu.(2021).Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions.IMA JOURNAL OF NUMERICAL ANALYSIS,41(2),1608-1638. |
| MLA | Hong, Jialin,et al."Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions".IMA JOURNAL OF NUMERICAL ANALYSIS 41.2(2021):1608-1638. |
入库方式： OAI收割
来源：数学与系统科学研究院
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