The full Brownian web as scalling limit of stochastic flows

Luiz Renato Fontes; Charles M. Newman

doi:10.1142/S0219493706001724

The full Brownian web as scalling limit of stochastic flows

Luiz Renato Fontes, Charles M. Newman

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	213-228
Number of pages	16
Journal	Stochastics and Dynamics
Volume	6
Issue number	2
DOIs	https://doi.org/10.1142/S0219493706001724
State	Published - 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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10.1142/S0219493706001724

Cite this

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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 Newman, {Charles M.}",

note = "Funding Information: The research of the authors was supported in part by the following sources: for L. R. F., FAPESP grant 04/07276-2 and CNPq grants 307978/2004-4 and 475833/2003-1; for C. M. N., grant DMS-01-04278 of the U.S. NSF. This paper has benefited from the hospitality shown to the authors at a number of venues where the research and writing took place, including the Courant Institute of Mathematical Sciences and the Ninth Brazilian School of Probability at Maresias Beach.",

year = "2006",

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doi = "10.1142/S0219493706001724",

language = "English (US)",

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pages = "213--228",

journal = "Stochastics and Dynamics",

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

AU - Fontes, Luiz Renato

AU - Newman, Charles M.

N1 - Funding Information: The research of the authors was supported in part by the following sources: for L. R. F., FAPESP grant 04/07276-2 and CNPq grants 307978/2004-4 and 475833/2003-1; for C. M. N., grant DMS-01-04278 of the U.S. NSF. This paper has benefited from the hospitality shown to the authors at a number of venues where the research and writing took place, including the Courant Institute of Mathematical Sciences and the Ninth Brazilian School of Probability at Maresias Beach.

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

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DO - 10.1142/S0219493706001724

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SN - 0219-4937

VL - 6

SP - 213

EP - 228

JO - Stochastics and Dynamics

JF - Stochastics and Dynamics

IS - 2

ER -

The full Brownian web as scalling limit of stochastic flows

Abstract

Keywords

ASJC Scopus subject areas

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