The full Brownian web as scalling limit of stochastic flows

Luiz Renato Fontes, Charles Newman

Research output: Contribution to journalArticle

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

Fingerprint

Stochastic Flow
Brownian movement
Trajectories
Path
Characterization Theorem
Rescaling
Convergence Theorem
Brownian motion
Space-time
Trajectory
Converge

Keywords

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

ASJC Scopus subject areas

  • Modeling and Simulation

Cite this

The full Brownian web as scalling limit of stochastic flows. / Fontes, Luiz Renato; Newman, Charles.

In: Stochastics and Dynamics, Vol. 6, No. 2, 06.2006, p. 213-228.

Research output: Contribution to journalArticle

@article{e36fd9cdfa5a401fa06746f9739b92ba,
title = "The full Brownian web as scalling limit of stochastic flows",
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.",
keywords = "Brownian web, Coalescing Brownian motions, Expansions and contractions, Full Brownian web, Scaling limit, Stochastic flows",
author = "Fontes, {Luiz Renato} and Charles Newman",
year = "2006",
month = "6",
doi = "10.1142/S0219493706001724",
language = "English (US)",
volume = "6",
pages = "213--228",
journal = "Stochastics and Dynamics",
issn = "0219-4937",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

TY - JOUR

T1 - The full Brownian web as scalling limit of stochastic flows

AU - Fontes, Luiz Renato

AU - Newman, Charles

PY - 2006/6

Y1 - 2006/6

N2 - 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.

AB - 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.

KW - Brownian web

KW - Coalescing Brownian motions

KW - Expansions and contractions

KW - Full Brownian web

KW - Scaling limit

KW - Stochastic flows

UR - http://www.scopus.com/inward/record.url?scp=33746310299&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746310299&partnerID=8YFLogxK

U2 - 10.1142/S0219493706001724

DO - 10.1142/S0219493706001724

M3 - Article

VL - 6

SP - 213

EP - 228

JO - Stochastics and Dynamics

JF - Stochastics and Dynamics

SN - 0219-4937

IS - 2

ER -