Asymptotic behaviour of mild solution of nonlinear stochastic partial functional equations driven by Rosenblatt process
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Date
2019-06-27
Journal Title
Journal ISSN
Volume Title
Publisher
Vilnius University Press
Abstract
This paper presents conditions to assure existence, uniqueness and stability for impulsive
neutral stochastic integrodifferential equations with delay driven by Rosenblatt process and Poisson jumps. The Banach fixed point theorem and the theory of resolvent operator developed by Grimmer [R.C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc., 273(1):333–349, 1982] are used. An example illustrates the potential benefits of these results.
Description
Stochastic differential equations (SDEs) arise in many areas of science and engineering,
wherein, quite often the future state of such systems depends not only on present state, but
also on its history leading to stochastic functional differential equations with delays rather
than SDEs.
Keywords
partial functional differential equations, existence result, resolvent operator, stability, Rosenblatt process, Poison jumps
Citation
Diop, M.A., Amoussou, A.T.G., Ogouyandjou, C., Sakthivel, R. (2019) Asymptotic behaviour of mild solution of nonlinear stochastic partial functional equations driven by Rosenblatt process, Nonlinear Analysis: Modelling and Control, Vol. 24, No. 4, pp.1–22. https://doi.org/10.15388/NA.2019.4.https://doi.org/10.15388/NA.2019.4.3