Title: A stochastic methodology for non-linear partial differential equations
Author: Christian Hesse

We study a class of non-linear partial differential equations with
non-negativity and integration conditions. Traditionally, these types
of equations have been solved numerically by means of non-stochastic
space-time discretization techniques such as finite differences or
finite elements. Here we aim to approximate the solutions by empirical
functionals of the dynamics of an appropriate system of interacting
particles whose evolution is governed by a system of coupled
stochastic differential equations. The latter are constructed in such
a way that the empirical densities of the interacting diffusion
processes approximate the corresponding solution of the original
partial differential equation. The approximation may be made as close
as desired if a sufficient number of diffusions is employed.