Resumen de Condiciones suficientes de estabilidad para ecuaciones en derivadas parciales estocásticas con retardos
Sufficient conditions for pathwise exponential stability of the zero solutions of stochastic PDE with deviating argument $dx_t =Ax_tdt +Bx_{\rho(t)}dw_t$ 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 $\rho(t)=t.$ First, we obtain sufficient conditions for the second moment of $x_t$ 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.
