Exponential stability for neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion

Abstract

In this paper, we study the exponential stability in the pth moment of mild solutions to neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion: where . Our method for investigating the stability of solutions is based on the Banach fixed point theorem. The obtained results generalize and improve the results due to Boufoussi and Hajji (Stat. Probab. Lett. 82:1549–1558, 2012), Caraballo et al. (Nonlinear Anal. 74:3671–3684, 2011), and Luo (J. Math. Anal. Appl. 355:414–425, 2009).

Stability of a Class of Impulsive Neutral Stochastic Functional Partial Differential Equations

“…Some sufficient conditions to ensure that the mild solution is exponentially stable in pth moment are established. e obtained results improve and generalize the results in [6,10,15,27]. In our next paper, we will investigate the global attracting set and quasi-invariant set of a class of neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion with impulses by means of the fixed point theorem.…”

“…en we conclude that (51) is weaker than (50); in this sense, this paper improves and generalizes the results in [27].…”

“…□ Remark 1. Zhang and Ruan in [27] considered (10) without impulsive effects and required the following conditions to ensure the pth (p ≥ 2) moment exponential stability:…”

“…In addition, similar phenomena have appeared in the research of fluid mechanics, electrical communication, economics, and finance. erefore, the mixed model has been considered by many authors; see, for example, [7,10,12,16,20,23,24,27].…”

“…It is important to consider the influence of delay and stochastic perturbations in the investigation of these systems. erefore, the stability of neutral stochastic functional partial differential equations has been studied by many researchers (see, for instance, [2,4,6,10,12,13,15,27] and the reference therein).…”