Abstract
In this paper we construct and provide a representation for a classical solution of some nonlinear SPDE driven by Fisk–Stratonovich stochastic integral. Our main assumption is the commuting property of the drift and diffusion vector fields with respect to the usual Lie bracket. This result is next applied for a system of Burgers equations with stochastic perturbations and also to the computations of some expectations of functionals depending on the final value of some non-Markovian process.
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