\(L^p(p > 2)\)-strong convergence of an averaging principle for two-time-scales jump-diffusion stochastic differential equations
type: Item
instance of: scholarly article
title: \(L^p(p > 2)\)-strong convergence of an averaging principle for two-time-scales jump-diffusion stochastic differential equations
zbMATH Open document ID: 1384.34070
author: Jie Xu
author: Yu Miao
published in: Nonlinear Analysis. Hybrid Systems
publication date: 2015-12-21T00:00:00Z
review text: The authors study the \(L^p\) (\(p > 2\))-strong convergence of the averaging principle (see [\textit{R. Z. Has'minskij}, Kybernetika 4, 260--279 (1968; Zbl 0231.60045)]) for a class of stochastic differential equations. In fact, under suitable conditions, it is shown that the slow component \(L^p\) \((p>2)\)-strongly converges to the solution of the corresponding averaging equation (Theorem 4.1). Their result extend some interesting results given by \textit{D. Liu} [Commun. Math. Sci. 8, No. 4, 999--1020 (2010; Zbl 1208.60057); Front. Math. China 7, No. 2, 305--320 (2012; Zbl 1255.60098)], \textit{D. Givon} et al. [Commun. Math. Sci. 4, No. 4, 707--729 (2006; Zbl 1115.60036)] or \textit{G. Wainrib} [Electron. Commun. Probab. 18, Paper No. 51, 12 p. (2013; Zbl 1297.70015)].
reviewed by: Romeo Negrea
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 6523030
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: stochastic averaging principle
zbMATH Keywords: \(L^p\)--strong convergence
MaRDI profile type: Publication
full work available at URL: j.nahs.2015.05.001
OpenAlex ID: W2250854382
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DOI: 10.1016/J.NAHS.2015.05.001
description: scientific article; zbMATH DE number 6523030