On the pth moment exponential stability criteria of neutral stochastic functional differential equations

Abstract

The paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the Ito type. This investigation can be very complicated, even in many special cases, by using usual methods based on Lyapunov functionals. In this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations.

Moment decay rates of stochastic differential equations with time-varying delay

“…Motivated by papers [3,4,16], for p ≥ 2 we can state a more effective and relatively easy way to verify criteria, in fact the consequences of Theorems 1-4, by taking particularly V (x, t) ≡ |x| p . Then, in view of (4),…”

Pth mean asymptotic stability and integrability of Itô-Volterra integrodifferential equations

“…It is well-known that there is significant and very rich literature discussing special techniques to study almost sure and pth mean exponential stability of solutions to various classes of stochastic differential equations (see monographs [12] and [15] by X. Mao, and [6,9,11,19], for instance). However, less attention has been devoted to asymptotic stability of Itô-Volterra integrodifferential equations (see [1,2,3,13,14] and literature cited therein, among other things).…”

Exponential stability behavior of neutral stochastic integrodifferential equations with fractional Brownian motion and impulsive effects

“…Meanwhile, they can be widely applied to many branches for the control field, including the problem of the existence and stability of the neutral stochastic delay systems [12]. So, many researchers have focused on the study of stability analysis of neutral stochastic delay systems during the last few decades [10,[13][14][15][16][17][18].…”