The \(p\)th moment exponential stability and almost surely exponential stability of stochastic differential delay equations with Poisson jump
type: Item
instance of: scholarly article
title: The \(p\)th moment exponential stability and almost surely exponential stability of stochastic differential delay equations with Poisson jump
zbMATH Open document ID: 1407.34113
author: Haidan Li
author: Quanxin Zhu
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-12-20T00:00:00Z
review text: In this paper the authors study a class of nonlinear stochastic differential delay equations with Poisson jump. By means of a Lyapunov function and the semi-martingale convergence theorem, they first prove the existence and uniqueness of a global solution under a local Lipschitz condition and a new nonlinear growth condition. Then some sufficient conditions ensuring the \(p\)-th moment and almost sure stability are established.
reviewed by: Xiaohu Wang
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 6996177
zbMATH Keywords: nonlinear stochastic differential delay equation
zbMATH Keywords: moment exponential stability
zbMATH Keywords: almost surely exponential stability
zbMATH Keywords: local Lipschitz condition
zbMATH Keywords: nonlinear growth condition
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.10.072
OpenAlex ID: W2899492954
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Wikidata QID: Q115570294
DOI: 10.1016/J.JMAA.2018.10.072
description: scientific article; zbMATH DE number 6996177