The Full Brownian Web as Scaling Limit of Stochastic Flows

Details The Full Brownian Web as Scaling Limit of Stochastic Flows The Full Brownian Web as Scaling Limit of Stochastic Flows

2005-11-01

arxiv.org/abs/math/0511029v2

Mathematics

Probability

18 pages, 1 figure

Scientific paper

In this paper we construct an object which we call the full Brownian web (FBW) and prove that the collection of all space-time trajectories of a class of one-dimensional stochastic flows converges weakly, under diffusive rescaling, to the FBW. The (forward) paths of the FBW include the coalescing Brownian motions of the ordinary Brownian web along with bifurcating paths. Convergence of rescaled stochastic flows to the FBW follows from general characterization and convergence theorems that we present here combined with earlier results of Piterbarg.

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