Refined basic couplings and Wasserstein-type distances for SDEs with Levy noises

doi:10.1016/j.spa.2018.09.003

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	Refined basic couplings and Wasserstein-type distances for SDEs with Levy noises
	Luo, Dejun1,2 ; Wang, Jian 3,4
	2019-09-01
发表期刊	STOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN	0304-4149
卷号	129 期号:9 页码:3129-3173
摘要	We establish the exponential convergence with respect to the L-1-Wasserstein distance and the total variation for the semigroup corresponding to the stochastic differential equation d X-t = d Z(t) + b(X-t) dt, where (Z(t))(t >= 0) is a pure jump Levy process whose Levy measure v fulfills inf(x is an element of Rd, vertical bar x vertical bar <=kappa 0) [v boolean AND (delta(x) (* )nu)](R-d) > 0 for some constant kappa(0) > 0, and the drift term b satisfies that for any x, y is an element of R-d, < b(x) - b(y), x - y > <= { Phi(1)(vertical bar x - y vertical bar) vertical bar x - y vertical bar, vertical bar x - y vertical bar < l(0); - K-2 vertical bar x - y vertical bar(2), vertical bar x - y vertical bar >= l(0) with some positive constants K-2, l(0) and positive measurable function Phi(1). The method is based on the refined basic coupling for Levy jump processes. As a byproduct, we obtain sufficient conditions for the strong ergodicity of the process (X-t)(t >= 0). (C) 2018 Elsevier B.V. All rights reserved.
关键词	Refined basic coupling Levy jump process Wasserstein-type distance Strong ergodicity
DOI	10.1016/j.spa.2018.09.003
语种	英语
资助项目	National Natural Science Foundation of China[11522106] ; National Natural Science Foundation of China[11831014] ; National Natural Science Foundation of China[11571347] ; National Natural Science Foundation of China[11688101] ; Youth Innovation Promotion Association, CAS[2017003] ; Special Talent Program of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences ; Fok Ying Tung Education Foundation[151002] ; Program for Probability and Statistics: Theory and Application[IRTL1704] ; Program for IRTSTFJ
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000482251600006
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35470
专题	应用数学研究所
通讯作者	Wang, Jian
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Fujian Normal Univ, Coll Math & Informat, Fuzhou 350007, Fujian, Peoples R China 4.Fujian Normal Univ, Fujian Key Lab Math Anal & Applicat FJKLMAA, Fuzhou 350007, Fujian, Peoples R China
推荐引用方式 GB/T 7714	Luo, Dejun,Wang, Jian. Refined basic couplings and Wasserstein-type distances for SDEs with Levy noises[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2019,129(9):3129-3173.
APA	Luo, Dejun,&Wang, Jian.(2019).Refined basic couplings and Wasserstein-type distances for SDEs with Levy noises.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,129(9),3129-3173.
MLA	Luo, Dejun,et al."Refined basic couplings and Wasserstein-type distances for SDEs with Levy noises".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 129.9(2019):3129-3173.