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A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
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Bloemker, D., Romito, M. and Tribe, Roger (2007) A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Volume 43 (Number 2). pp. 175-192. doi:10.1016/j.anihpb.2006.02.001 ISSN 0246-0203.
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Official URL: http://dx.doi.org/10.1016/j.anihpb.2006.02.001
Abstract
The solutions to a large class of non-linear parabolic PDEs are given in terms of expectations of suitable functionals of a tree of branching particles. A sufficient, and in some cases necessary, condition is given for the integrability of the stochastic representation, using a comparison scalar PDE.
In cases where the representation fails to be integrable, a sequence of pruned trees is constructed, producing approximate stochastic representations that in some cases converge, globally in time, to the solution of the original PDE. (c) 2006 Elsevier Masson SAS.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques | ||||
Publisher: | Institute Henri Poincaré | ||||
ISSN: | 0246-0203 | ||||
Official Date: | 2007 | ||||
Dates: |
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Volume: | Volume 43 | ||||
Number: | Number 2 | ||||
Number of Pages: | 18 | ||||
Page Range: | pp. 175-192 | ||||
DOI: | 10.1016/j.anihpb.2006.02.001 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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