The Brownian net

Abstract

The (standard) Brownian web is a collection of coalescing one- dimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. We show that it is possible to obtain a nontrivial limiting object if the random walks in addition branch with a small probability. We call the limiting object the Brownian net, and study some of its elementary properties.

Published in at http://dx.doi.org/10.1214/07-AOP357 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• The Brownian web: Characterization and convergence
• Consistent families of Brownian motions and stochastic flows of kernels

Cited by in corpus (1)

• Consistent families of Brownian motions and stochastic flows of kernels