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arXiv · 1610.00481

Superprocesses on ultradistributions

R. Vilela Mendes
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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: McKean's and superprocesses. In favour of superprocesses is the fact that they handle arbitrary boundary conditions. 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 ultradistributions, is proposed to extend the stochastic solution approach to a wider class of PDE's.

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BibTeXRIS

R. Vilela Mendes. 2016-10-03. Superprocesses on ultradistributions. https://doi.org/10.1080/17442508.2016.1269768

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