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The goal of the paper is to show, under possibly weak assumptions, that thefunction given by the Feynman-Kac formula is a classical solution of theassociated Kolmogorov equation. We also show that although this solution isunbounded it fulfills Schauder's estimates. The paper collects mostly knownresults on the regularity of solutions of linear parabolic equations of secondorder and the regularity of solutions of Ito stochastic differential equations.We aim to reproduce these and related results in a unified fashion.

Partial Schauder estimates for unbounded solutions of the Kolmogorov equation