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.
A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees / D. BLOEMKER; M. ROMITO; R. TRIBE. - In: ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. - ISSN 0246-0203. - STAMPA. - 43:(2007), pp. 175-192. [10.1016/j.anihpb.2006.02.001]
A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
ROMITO, MARCO;
2007
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.File | Dimensione | Formato | |
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