Approximate evaluation of wiener continual integrals by the Monte Carlo method

A class of approximate expressions, exact for all polynomial functions of up to and including the third degree, and for certain other functionals of special type, is considered for the evaluation of Wiener continual integrals. A number of generalizations of Cameron's expressions is obtained, whereby the accuracy can be improved withour increasing the complexity of the approximate formula. Special approximations of the Wiener process are described, whereby estimates of the Monte Carlo method with minimum variance can be constructed. Examples are given of the evaluation of Wiener integrals of certain functionals, and in particular, of the functional describing the motion of an electron in a polar crystal.