SOLUCIÓN PERIÓDICA DE LAS ECUACIONES ESTOCÁSTICAS CON COEFICIENTES DIFINIDOS EN UNA UNIÓN DE INTERVALOS CERRADOS

Abstract

In this article we consider a class of stochastic equations with coefficients defined on a union of closed time intervals; during the break between two closed intervals the process has to evolve passively with the coefficients determined at the last moment of the previous closed interval. Under the assumption of the periodicity of the union of closed intervals and of the coefficients, we prove the existence of a
periodic solution. The proof is based on the techniques developed by Khas’minskii for the analogous problem in case of usual stochastic equations. We present also some remarks about the possibility of application to the stochastic modeling of the hibernation