Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions

doi:10.1093/imanum/draa019

CSpace

	Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions
	Hong, Jialin ; Huang, Chuying 1; Wang, Xu
	2021-04-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	41 期号:2 页码:1608-1638
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.
关键词	fractional Brownian motion strong convergence rate Runge-Kutta method simplified step-N Euler scheme
DOI	10.1093/imanum/draa019
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[11871068]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000651815700026
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58702
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.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, 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	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.