The stability of stochastic partial differential equations II

Abstract

We prove general results on stability (in finite time intervals) of SPDEs (stochastic partial differential equations) with unbounded coefficients, with respect to the simultaneous perturbations of the driving semimartingales, of all data, and of the underlying probability space. Hence we derive support theorems for SPDEs (with unbounded coefficients). In particular, we get theorems on supports and theorems on robustness for the nonlinear filter of diffusion processes with unbounded drift and diffusion coefficients. (The above results were proved in the case of bounded coefficients in our earlier papers [4] and [5].) Finally we treat an application in a problem of kinematic dynamo

Keywords:

• SPDE
• Sobolev spaces
• semimartingale
• nonlinear filtering

^*The results of this paper were presented in the IFIP-WG7.7. Conference on Optimization in Stochastic Systems,held in Debrecen (Hungry),June 27-30,1988.

^*The results of this paper were presented in the IFIP-WG7.7. Conference on Optimization in Stochastic Systems,held in Debrecen (Hungry),June 27-30,1988.

Notes

^*The results of this paper were presented in the IFIP-WG7.7. Conference on Optimization in Stochastic Systems,held in Debrecen (Hungry),June 27-30,1988.