Exponential stability for some stochastic neutral partial functional integrodifferential equations with delays and Poisson jumps
type: Item
instance of: scholarly article
title: Exponential stability for some stochastic neutral partial functional integrodifferential equations with delays and Poisson jumps
zbMATH Open document ID: 1302.45020
author: Mamadou Abdoul Diop
author: Khalil Ezzinbi
author: Modou Lo
published in: Semigroup Forum
publication date: 2014-09-12T00:00:00Z
review text: The paper deals with stochastic neutral partial functional integro-differential equations with delays in a real separable Hilbert space. The noise term is represented by a Wiener process and Poisson jumps. The main result of the paper, Theorem 3.1, gives sufficient conditions for the existence and exponential stability in the mean square sense of mild solutions to the equations under consideration. The main result is proved under the assumption that the linear part of the equations has a resolvent operator. The proof of the result is given in details. It is based on the Banach fixed point principle. The paper seems to be an interesting contribution to current stability theory of stochastic equations. Moreover, in the paper an application of the results obtained is provided. The references cited in the paper are representative enough for the problem studied.
reviewed by: Anna Karczewska
Mathematics Subject Classification ID: 45R05
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 6343958
zbMATH Keywords: neutral partial functional integro-differential equations
zbMATH Keywords: exponential stability in the mean square sense
zbMATH Keywords: resolvent operators
zbMATH Keywords: Wiener process
zbMATH Keywords: Poisson jumps
zbMATH Keywords: Picard iteration
zbMATH Keywords: mild solution
zbMATH Keywords: Banach fixed point principle
MaRDI profile type: Publication
full work available at URL: s00233-013-9555-y
OpenAlex ID: W2047787728
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DOI: 10.1007/S00233-013-9555-Y
description: scientific article; zbMATH DE number 6343958