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.

In this paper, we study the almost sure moment exponential stability of mild solutions of stochastic neutral partial functional differential equations in real separable Hilbert spaces using local Lipschitz conditions. Even in the special case, when the neutral term is zero, the results obtained here appear to be new and complement the study in [Taniguchi, et al, J. Differential Eqns. 181 (2002)...

Stochastic effects on convergence dynamics of reaction-diffusion Cohen-Grossberg neural networks CGNNs with delays are studied. By utilizing Poincaré inequality, constructing suitable Lyapunov functionals, and employing the method of stochastic analysis and nonnegative semimartingale convergence theorem, some sufficient conditions ensuring almost sure exponential stability and mean square expon...

This paper examines the numerical solutions of neutral stochastic functional differential equation. study establishes discrete Razumikhin-type theorem to investigate exponential stability in mean square sense Euler–Maruyama solution this In addition, Borel–Cantelli lemma and analysis theory are incorporated discuss almost sure for such equations.