Path Integral Transformations and Stochastic Processes

Authors: S. N. STORCHAK

Abstract: The path integral transformation that changes the evolution parameters of the paths is considered in the path integrals for the systems of two differential equations in one space dimension and in the path integrals related with the fourth-order linear parabolic differential equations. In both cases, the coefficients of differential equations have an explicit time dependence. By using the procedure of the stochastic change of time and phase-space transformation of the stochastic processes the integral relations between the Green functions of the corresponding differential equations have been obtained. As a consequence the generalization of the Shepp formula for the Green function is obtained. It is shown, that paths reparametrization in the higher-order path integrals leads to the Green function for the differential equation with the Bol operator.