Stochastic solutions of nonlinear PDE's and an extension of superprocesses

Abstract: Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions: MacKean's and superprocesses. However, when restricted to measures, superprocesses can only be used to generate solutions for a limited class of nonlinear PDE's. A new class of superprocesses, namely superprocesses on signed measures and on distributions, is proposed to extend the stochastic solution approach to a wider class of PDE's.