Asymptotic behavior of neutral stochastic
This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H ∈ (12, 1). The main tools for the existence of solution is a fixed point theorem and the theory of resolvent operators developed in Grimmer [R. Grimmer, Trans. Amer. Math. Soc., 273 (1982), 333–349.], while a Gronwall-type lemma plays the key role for the asymptotic behavior. An example is provided to illustrate the results of this work. (c) 2014 All rights reserved.
Resolvent operators, C0-semigroup, Wiener process, Mild solutions, Fractional Brownian motion, Exponential decay of solutions
T. Caraballo, M. A. Diop, A. A. Ndiaye, J. Nonlinear Sci. Appl. 7 (2014), 407–421. DOI: 10.22436/jnsa.007.06.04