Weak order in averaging principle for stochastic differential equations with jumps

Abstract In this paper, we deal with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equations. Under suitable conditions, we expand the weak error in powers of timescale parameter. We prove that the rate of weak convergence to the averaged dynamics is o...

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Main Authors:	Bengong Zhang, Hongbo Fu, Li Wan, Jicheng Liu
Format:	Article
Language:	English
Published:	SpringerOpen 2018-05-01
Series:	Advances in Difference Equations
Subjects:	Jump-diffusion Averaging principle Invariant measure Weak convergence Asymptotic expansion
Online Access:	http://link.springer.com/article/10.1186/s13662-018-1638-3

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spelling	doaj-5b5b6758b35d4b4685825da18d4e37ce2020-11-25T00:37:36ZengSpringerOpenAdvances in Difference Equations1687-18472018-05-012018112010.1186/s13662-018-1638-3Weak order in averaging principle for stochastic differential equations with jumpsBengong Zhang0Hongbo Fu1Li Wan2Jicheng Liu3College of Mathematics and Computer Science, Wuhan Textile UniversityCollege of Mathematics and Computer Science, Wuhan Textile UniversityCollege of Mathematics and Computer Science, Wuhan Textile UniversitySchool of Mathematics and Statistics, Huazhong University of Science and TechnologyAbstract In this paper, we deal with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equations. Under suitable conditions, we expand the weak error in powers of timescale parameter. We prove that the rate of weak convergence to the averaged dynamics is of order 1. This reveals that the rate of weak convergence is essentially twice that of strong convergence.http://link.springer.com/article/10.1186/s13662-018-1638-3Jump-diffusionAveraging principleInvariant measureWeak convergenceAsymptotic expansion
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bengong Zhang Hongbo Fu Li Wan Jicheng Liu
spellingShingle	Bengong Zhang Hongbo Fu Li Wan Jicheng Liu Weak order in averaging principle for stochastic differential equations with jumps Advances in Difference Equations Jump-diffusion Averaging principle Invariant measure Weak convergence Asymptotic expansion
author_facet	Bengong Zhang Hongbo Fu Li Wan Jicheng Liu
author_sort	Bengong Zhang
title	Weak order in averaging principle for stochastic differential equations with jumps
title_short	Weak order in averaging principle for stochastic differential equations with jumps
title_full	Weak order in averaging principle for stochastic differential equations with jumps
title_fullStr	Weak order in averaging principle for stochastic differential equations with jumps
title_full_unstemmed	Weak order in averaging principle for stochastic differential equations with jumps
title_sort	weak order in averaging principle for stochastic differential equations with jumps
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2018-05-01
description	Abstract In this paper, we deal with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equations. Under suitable conditions, we expand the weak error in powers of timescale parameter. We prove that the rate of weak convergence to the averaged dynamics is of order 1. This reveals that the rate of weak convergence is essentially twice that of strong convergence.
topic	Jump-diffusion Averaging principle Invariant measure Weak convergence Asymptotic expansion
url	http://link.springer.com/article/10.1186/s13662-018-1638-3
work_keys_str_mv	AT bengongzhang weakorderinaveragingprincipleforstochasticdifferentialequationswithjumps AT hongbofu weakorderinaveragingprincipleforstochasticdifferentialequationswithjumps AT liwan weakorderinaveragingprincipleforstochasticdifferentialequationswithjumps AT jichengliu weakorderinaveragingprincipleforstochasticdifferentialequationswithjumps
_version_	1725300489339273216

Weak order in averaging principle for stochastic differential equations with jumps

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