Approximate solution of multidimensional Kolmogorov equation using Feynman-Chernoff iterations

In this paper we propose a new algorithm for the numerical approximation of solutions to the multidimensional Kolmogorov equation, based on the averaging of Feynman-Chernoff iterations for random operator-valued functions. In the case when the values of operator-valued functions belong to the representation of some finite-dimensional Lie group, the proposed algorithm has a lower computational complexity compared to the standard Monte Carlo algorithm that uses the Feynman-Kac formula. In particular, we study the case of a group of affine transformations of a Euclidean space. For the considered algorithms we also present the results of numerical calculations.