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

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

2005-05-21

arxiv.org/abs/math/0505449v1

Mathematics

Probability

Scientific paper

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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