Mixed Neutral Caputo Fractional Stochastic Evolution Equations with Infinite Delay: Existence, Uniqueness and Averaging Principle

Abstract

The aim of this article is to consider a class of neutral Caputo fractional stochastic evolution equations with infinite delay (INFSEEs) driven by fractional Brownian motion (fBm) and Poisson jumps in Hilbert space. First, we establish the local and global existence and uniqueness theorems of mild solutions for the aforementioned neutral fractional stochastic system under local and global Carathéodory conditions by using the successive approximations, stochastic analysis, fractional calculus, and stopping time techniques. The obtained existence result in this article is new in the sense that it generalizes some of the existing results in the literature. Furthermore, we discuss the averaging principle for the proposed neutral fractional stochastic system in view of the convergence in mean square between the solution of the standard INFSEEs and that of the simplified equation. Finally, the obtained averaging theory is validated with an example.

Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process

“…for all t, v ≥ 0. Note that, when H = 1 2 , S H corresponds to the well known Brownian motion B. Sub-fractional Brownian motion has properties that are similar to those of fractional Brownian motion, such as the following: long-range dependence, Self-similarity, Hölder pathes, and it satisfies [17][18][19][20][21][22][23].…”

Multivalued Impulsive SDEs Driven by G‐Brownian Noise: Periodic Averaging Result

“…Te theory of averaging principles provides a useful account of how to simplify the complex systems to be more amenable in numerical calculations and analysis. Recently, a considerable amount of literature has emerged around the theme of approximation theorems for stochastic diferential equations (SDEs) [1][2][3][4][5][6][7][8]. As one of the most signifcant models, recently, multivalued stochastic diferential equations (MSDEs) received considerable critical attention.…”