Stochastic solutions of nonlinear PDE's and an extension of superprocesses
Mathematical Physics
2012-09-17 v1 math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1209.3263,
title = {Stochastic solutions of nonlinear PDE's and an extension of superprocesses},
author = {Rui Vilela Mendes},
journal= {arXiv preprint arXiv:1209.3263},
year = {2012}
}
Comments
11 pages. arXiv admin note: substantial text overlap with arXiv:1111.5504