Asymptotic behaviour of mild solution - Diop, Mamadou Abdoul; Amoussoub, Amour Toffodji Gbaguidi; Ogouyandjou, Carlos; Sakthivel, Rathinasam (Vilnius University Press, 2019)
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.
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