ON THE STABILITY OF THE SOLUTION FOR THE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

The stability of the solution for the stochastic partial differential equation is considered in this paper, when the initial condition and the coefficients of the first and seeond order differential operators are subject to small perturbations. Also discussed is the stability of the Zakai equation which is a stochastic partial differential equation for measure valued process ari sing in non-linear filtering theory. The powerful tools are the theory of backward stochastic Stratonovioh differontial equations and Ito’s baokward formula.