arXiv math/05054492005-05-21math.PRmath-phmath.MP

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

D. Blömker, M. Romito, R. Tribe

英文摘要：

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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