Partial stability analysis of stochastic differential equations with a general decay rate

Stability criteria of stochastic partial differential equations with variable delays∗

Abstract. Some criteria for the asymptotic stability of nonlinear stochastic partial differential equations with variable delays are presented. A coercivity condition plays the role of an exponential stability criterion. Consequently, under the coercivity condition almost all the trajectories of the nonstationary solutions of the given stochastic system finally tend exponentially to zero. Two e...

General Decay Stability for Stochastic Functional Differential Equations with Infinite Delay

So far there are not many results on the stability for stochastic functional differential equations with infinite delay. Themain aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay ...

Stochastic Partial Differential Equations

The Exponential Stability of Neutral Stochastic Delay Partial Differential Equations

In this paper we analyse the almost sure exponential stability and ultimate boundedness of the solutions to a class of neutral stochastic semilinear partial delay differential equations. This kind of equations arises in problems related to coupled oscillators in a noisy environment, or in viscoeslastic materials under random or stochastic influences.

Asymptotic Stability of Stochastic Impulsive Neutral Partial Functional Differential Equations

In this paper the authors study the existence and asymptotic stability in p-th moment of mild solutions to stochastic neutral partial differential equation with impulses. Their method for investigating the stability of solutions is based on the fixed point theorem.