Abstract
Stochastic solutions provide new rigorous results for nonlinear PDE’s and, through its local nongrid 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.
Notes
No potential conflict of interest was reported by the author.
1 For a detailed account of the nature of the limitations of superprocesses on measures as related to the positivity of the coefficients in the offspring generating function, see [Citation26].
2 Distributions which locally are , f bounded and continuous.
3 These two examples had been described at an heuristic level in the conference paper [Citation24]. However, their rigorous proof depended on the establishment of Proposition 1.