Feynman-Kac formulas for evolution differential equations with white-noise-type coefficients (Q1594441)

The main result of this paper is a representation of the solution of Cauchy problems for second-order evolution stochastic differential equations by integrals with respect to measures in the configuration and momentum spaces. The first representation is similar to that of Doss in the nonstochastic case; it uses integration with respect to the Wiener measure in the space of trajectories in the configuration space. The second one is the stochastic version of a Maslov's result, using integration with respect to Poisson-type measure in the space of trajectories in the momentum space. Both representations are derived by using the Fourier transform of the measures corresponding to the random processes.