2005/05/21 by D. Blömker, Dirk Blömker, M. Romito +6
Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #35C99 #35K55 #35Q30 #60H30 #60J80 #76M35 #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications #math-ph #math.MP #math.PR #msc:35C99 #msc:35K55 #msc:35Q30 #msc:60H30 #msc:60J80 #msc:76M35
paper · pdf · doi:10.48550/arxiv.math/0505449
arxiv created 2005/05/21 · openalex publication_date 2005/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.