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

Yue Liu,Dehao Ruan

doi:10.1155/2020/9051396

Abstract

In this paper, a class of impulsive neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion is investigated. Under some suitable assumptions, the pth moment exponential stability is discussed by means of the fixed-point theorem. Our results also improve and generalize some previous studies. Moreover, one example is given to illustrate our main results.

Highlights

In recent years, stochastic differential equations (SDEs) have come to play an important role in many areas such as physics, population dynamics, electrical engineering, medicine biology, ecology, economics and other areas of science, and engineering
The random perturbation of stock prices consists of two parts: one is the basic part, that is, the overall economic situation of the society, comes from the actual financial background of the stock market and has a long correlation, so it can be expressed by fractional Brownian motion; the other is trading part, that is, the random trading conditions of stockholders in the stock market, is derived from the stochastic inherent factors of stockholders, so it can be expressed by Brownian motion
Motivated by the above discussion, this paper is concerned with the exponential stability results for a class of neutral stochastic functional partial differential equations driven by standard Brownian motion and fractional Brownian motion with impulses:

Summary

Introduction

Stochastic differential equations (SDEs) have come to play an important role in many areas such as physics, population dynamics, electrical engineering, medicine biology, ecology, economics and other areas of science, and engineering. Motivated by the above discussion, this paper is concerned with the exponential stability results for a class of neutral stochastic functional partial differential equations driven by standard Brownian motion and fractional Brownian motion with impulses:.

Preliminaries

The pth Moment Exponential Stability

Example

Conclusion