Multi-Scaling of the $n$-point density function for coalescing Brownian motions
This paper gives a derivation for the large time asymptotics of the $n$-point density function of a system of coalescing Brownian motions on $\bf{R}$.
math.PR↗
arXiv subjects
R. Tribe
Publications and source records attributed to R. Tribe.
A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
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.
math.PR↗