Feynman Formulas for Solutions to Evolution Equations in Domains of Multidimensional Ramified Surfaces

Abstract

Solutions of second-order parabolic differential equations for functions defined in domains of a K ramified surface in the class L₂(K) are obtained. With the help of Chernoff’s theorem, such solutions (if they exist) can be represented in the form of Lagrangian Feynman formulas, i.e., in the form of limits of integrals over Cartesian powers of the configuration space as the number of factors tends to infinity.