Stochastic Feynman-Kac formula (Q794347)

The stochastic partial differential equation called stochastic Feynman- Kac formula is investigated. For any distribution \(g\in {\mathcal D}'(R^ d)\) the author proves that the equation has a unique solution g exp- \(\int^{t}_{0}V(\cdot +w_ s)ds\) defining a semimartingale with the strong Markov property with continuous trajectories in \({\mathcal D}'(R^ d)\), and the infinitesimal generator of the semigroup is explicitly evaluated. Similar methods are applied to the Schrödinger equation.