The full Brownian web as scalling limit of stochastic flows

Luiz Renato Fontes, Charles M. Newman

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we construct an object which we call the full Brownian web (FBW) and prove that the collection of all spacetime 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.

Original languageEnglish (US)
Pages (from-to)213-228
Number of pages16
JournalStochastics and Dynamics
Volume6
Issue number2
DOIs
StatePublished - Jun 2006

Keywords

  • Brownian web
  • Coalescing Brownian motions
  • Expansions and contractions
  • Full Brownian web
  • Scaling limit
  • Stochastic flows

ASJC Scopus subject areas

  • Modeling and Simulation

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