Jump-type processes and their applications in quantum mechanics

A survey is presented of mathematical methods in the theory of the Feynman path integral. Principal attention is devoted to new results making it possible to represent the solution of the Cauchy problem for the Schrödinger equation and a quasilinear equation of Hartree type in the form of the mathematical expectation of functionals on jump-type Markov processes and to use Monte Carlo methods for solving these equations. A brief survey of results on complex Markov chains is presented.