A d-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process

Xavier Bardina; Carles Rovira

doi:https://doi.org/10.1007/s10986-013-9190-z

A d-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process

Xavier Bardina, Carles Rovira

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

We show how from a unique standard Poisson process we can build a family of processes that converges in law to a d-dimensional standard Brownian motion for any d ≥ 1. © 2013 Springer Science+Business Media New York.

Original language	English
Pages (from-to)	17-26
Journal	Lithuanian Mathematical Journal
Volume	53
DOIs	https://doi.org/10.1007/s10986-013-9190-z
Publication status	Published - 12 Mar 2013

Keywords

Poisson process
d-dimensional Brownian motion
weak approximations

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https://doi.org/10.1007/s10986-013-9190-z

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title = "A d-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process",

abstract = "We show how from a unique standard Poisson process we can build a family of processes that converges in law to a d-dimensional standard Brownian motion for any d ≥ 1. {\textcopyright} 2013 Springer Science+Business Media New York.",

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author = "Xavier Bardina and Carles Rovira",

year = "2013",

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AU - Rovira, Carles

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N2 - We show how from a unique standard Poisson process we can build a family of processes that converges in law to a d-dimensional standard Brownian motion for any d ≥ 1. © 2013 Springer Science+Business Media New York.

AB - We show how from a unique standard Poisson process we can build a family of processes that converges in law to a d-dimensional standard Brownian motion for any d ≥ 1. © 2013 Springer Science+Business Media New York.

KW - Poisson process

KW - d-dimensional Brownian motion

KW - weak approximations

U2 - https://doi.org/10.1007/s10986-013-9190-z

DO - https://doi.org/10.1007/s10986-013-9190-z

M3 - Article

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SP - 17

EP - 26

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

SN - 0363-1672

ER -

A d-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process

Abstract

Keywords

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