A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees

D. Blömker; M. Romito; R. Tribe

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A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees

D. Blömker·M. Romito·R. Tribe

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Abstract

The solutions to a large class of semi-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 companion scalar PDE. In cases where the representation fails to be integrable a sequence of pruned trees is constructed, producing a approximate stochastic representations that in some cases converge, globally in time, to the solution of the original PDE.

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BibTeX RIS

D. Blömker, M. Romito, R. Tribe. 2005-05-21. A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees. https://arxiv.org/abs/math/0505449

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