A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
概率论
2007-05-23 v1 数学物理
math.MP
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.
关键词
引用
@article{arxiv.math/0505449,
title = {A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees},
author = {D. Blömker and M. Romito and R. Tribe},
journal= {arXiv preprint arXiv:math/0505449},
year = {2007}
}