Condiciones suficientes de estabilidad para Ecuaciones en Derivadas Parciales estocásticas con retardos

Abstract

Sufficient conditions for pathwise exponential stability of the zero solution of stochastic PDE with deviating argument dxt = Axt dt + Bx (t) dwt are given.

The assumptions on the operators A and B are the same that in the case without delay, but the proof is different. In fact, our method shows an alternative proof for the results in the particular case (t) = t : First, we obtain su cient conditions for the second moment of xt to decay exponentially. Next, asymptotic exponential stability of paths (with probability one) is deduced. Finally,an example is given in order to illustrate our theory.