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arXiv:1209.3263 [math-ph]AbstractReferencesReviewsResources

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

Rui Vilela Mendes

Published 2012-09-14Version 1

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.

Comments: 11 pages. arXiv admin note: substantial text overlap with arXiv:1111.5504
Categories: math-ph, math.MP, math.PR
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