Morozov

Cauchy-Neyman problem for parabolic equation on half-line with variable coefficients depending on coordinate was considered.Solution of this problem was presented as a limit of elementary multiple integrals, containing coefficients of equation and initial conditions, when multiple approached infinity. Such formulas were called “Feynman’s formulas”. Similar presentations of evolution equations’ solutions could be used for direct computation and computer simulation of researched dynamics. Among other things, limits of finite-multiplicity integrals in Feynman’s formulas agreed with some functional integrals in some probability measures on set of trajectories in the areas where equations were considered. By this means, Feynman’s formulas allowed to approximate functional integrals and, consequently, transition probabilities (which usually weren’t expressed in terms of elementary functions) of corresponding random processes. Method for obtaining Feynman’s formulas for evolution equations has been proposed in the works of Smolyanov O. G. and his co-authors in 1999 – 2003 years. This method was based on the application of Chernoff’s theorem and allowed to obtain Feynman’s and Feynman-Katz’s formulas for extensive class of evolution equations on different geometric structures.