RAZUMIKHIN-TYPE THEOREMS ON EXPONENTIAL STABILITY OF STOCHASTIC FUNCTIONAL-DIFFERENTIAL EQUATIONS

Although the Razumikhin-type theorems have been well developed for the stability of functional differential equations and they are very usef ul in applications, so far there is almost no result of Razumikhin typ e on the stability of stochastic functional differential equations. Th e main aim of this paper is to close this gap by establishing several Razumikhin-type theorems on the exponential stability for stochastic f unctional differential equations. By applying these new results to sto chastic differential delay equations and stochastically perturbed equa tions we improve or generalize several known results, and this shows t he powerfulness of our new results clearly.