The stability of stochastic partial differential equations and applications i

We investigate the stability of stochastic evolution equations with respect to simultaneous perturbations of the driving semimartingales, of all data (on finite time intervals), and of the probability space. The result we present generalises earlier work of the author. As applications we prove Stroock-Varadhan type theorems on the supports for stochastic evolution equations. In Part II of this sequel we shall apply the results of the present paper (Part I) to stochastic partial differential equations, in particular we deal with applications in nonlinear filtering and in a problem of kinematic dynamo