Freidlin M. Functional Integration and Partial Differential Equations

Princeton University Press, Princeton, 1985. — 558 p.With every second-order elliptic differential operator L, one can associate a family of probability measures in the space of continuous functions on the half-line. This family of measures forms the Markov process corresponding to the Markov operator L.
This book considers problems arising in the theory of differential equations. Markov processes (or the corresponding families of measures in the space of continuous functions) are here only a tool for examining differential equations.
This book is intended not only for mathematicians specializing in the theory of differential equations or in probability theory but also for specialists in asymptotic methods and functional analysis. The book may also be of interest to physicists using functional integration in their research.Stochastic differential equations and related topics.
Representation of solutions of differential equations as functional integrals and the statement of boundary value problems.
Boundary value problems for equations with non-negative characteristic form.
Small parameter in second-order elliptic differential equations.
Quasi-linear parabolic equations with non-negative characteristic form.
Quasi-linear parabolic equations with small parameter. Wave fronts propagation.
Wave front propagation in periodic and random media.