Abstract
In this paper we present a general result on the stability of stochastic evolution equations and of stochastic partial differential equations with respect to the simultaneous perturbations of the driving semimartingales and of the unbounded operators in the equations, in the topology of uniform convergence on finite time intervals in probability. Hence we obtain theorems on supports for stochastic evolution equations and stochastic partial differential equations. These results are generalizations of the Stroock-Varadhan support theorem of diffusion processes. As applications, we prove theorems on supports for the nonlinear filter in the filtering theory of diffusion processes.
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