Allognissode, F.K, Diop, M.A, Ezzinbi, K, Ogouyandjou, C. (2019) Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior, Random Operators and Stochastic Equations. https://doi.org/10.1515/rose-2019-2009 - Allognissode, Fulbert Kuessi; Diop, Mamadou Abdoul; Ezzinbi, Khalil; Ogouyandjou, Carlos (De Gruyter, 2019)
This paper deals with the existence and uniqueness of mild solutions to stochastic partial functional integro-differential equations driven by a sub-fractional Brownian motion S[H/Q] (t), with Hurst parameter H∈(1\2,1). By the theory of resolvent operator developed by R. Grimmer (1982) to establish the existence of mild solutions, we give sufficient conditions ensuring the existence, uniqueness and the asymptotic behavior of the mild solutions. An example is provided to illustrate the theory.
Keywords: Existence and uniqueness; stochastic delay evolution equations; exponential decay in mean square; Resolvent operators; Wiener process; mild solutions; mild solutions