Discrete and Continuous Dynamical Systems · 2007 · 67 citations · 0 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsStochastic ProcessesContinuous-time Stochastic ProcessesPartial Differential EquationsStability TheoryStochastic CalculusStochastic Differential EquationsStochastic StabilityAlmost Sure StabilityExponential StabilityNeutral Delay SystemsStability Of Delay Differential EquationsStability Of Neutral Differential EquationsStochastic Delay SystemsStochastic Differential SystemsStochastic Partial Differential Equations
In this paper we analyze the almost sure exponential stability andultimate boundedness of the solutions to a class of neutralstochastic semilinear partial delay differential equations. Thesekind of equations arise in problems related to coupled oscillatorsin a noisy environment, or in viscoeslastic materials under randomor stochastic influences.