Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes

Xavier Bardina; Maria Jolis; Ciprian Tudor

doi:https://doi.org/10.1016/j.spl.2003.09.001

Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes

Xavier Bardina, Maria Jolis, Ciprian Tudor

Department of Mathematics

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

22 Citations (Scopus)

Abstract

We give a result of approximation in law, in the space of the continuous functions on [0,1] 2 , of Gaussian two-parameter processes that can be represented in law as a certain Wiener-type integral. The approximations are constructed from a Poisson process in the plane. © 2003 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	317-329
Journal	Statistics and Probability Letters
Volume	65
DOIs	https://doi.org/10.1016/j.spl.2003.09.001
Publication status	Published - 15 Dec 2003

Keywords

Fractional Brownian sheet
Two-parameter Gaussian processes
Two-parameter Poisson process
Weak convergence

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https://doi.org/10.1016/j.spl.2003.09.001

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title = "Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes",

abstract = "We give a result of approximation in law, in the space of the continuous functions on [0,1] 2 , of Gaussian two-parameter processes that can be represented in law as a certain Wiener-type integral. The approximations are constructed from a Poisson process in the plane. {\textcopyright} 2003 Elsevier B.V. All rights reserved.",

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author = "Xavier Bardina and Maria Jolis and Ciprian Tudor",

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T1 - Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes

AU - Bardina, Xavier

AU - Jolis, Maria

AU - Tudor, Ciprian

PY - 2003/12/15

Y1 - 2003/12/15

N2 - We give a result of approximation in law, in the space of the continuous functions on [0,1] 2 , of Gaussian two-parameter processes that can be represented in law as a certain Wiener-type integral. The approximations are constructed from a Poisson process in the plane. © 2003 Elsevier B.V. All rights reserved.

AB - We give a result of approximation in law, in the space of the continuous functions on [0,1] 2 , of Gaussian two-parameter processes that can be represented in law as a certain Wiener-type integral. The approximations are constructed from a Poisson process in the plane. © 2003 Elsevier B.V. All rights reserved.

KW - Fractional Brownian sheet

KW - Two-parameter Gaussian processes

KW - Two-parameter Poisson process

KW - Weak convergence

U2 - https://doi.org/10.1016/j.spl.2003.09.001

DO - https://doi.org/10.1016/j.spl.2003.09.001

M3 - Article

SN - 0167-7152

VL - 65

SP - 317

EP - 329

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes

Abstract

Keywords

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