Approximations of fractional Brownian motion

Yuqiang Li; Hongshuai Dai

doi:10.3150/10-BEJ319

Approximations of fractional Brownian motion

Yuqiang Li^*
, Hongshuai Dai

^*Corresponding author for this work

School of Statistics

School of Mathematics and Statistics

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

21 Scopus citations

Abstract

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.

Original language	English
Pages (from-to)	1195-1216
Number of pages	22
Journal	Bernoulli
Volume	17
Issue number	4
DOIs	https://doi.org/10.3150/10-BEJ319
State	Published - Nov 2011

Keywords

Fractional Brownian motion
Poisson process
Weak convergence

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10.3150/10-BEJ319

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title = "Approximations of fractional Brownian motion",

abstract = "Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.",

keywords = "Fractional Brownian motion, Poisson process, Weak convergence",

author = "Yuqiang Li and Hongshuai Dai",

year = "2011",

month = nov,

doi = "10.3150/10-BEJ319",

language = "英语",

volume = "17",

pages = "1195--1216",

journal = "Bernoulli",

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number = "4",

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T1 - Approximations of fractional Brownian motion

AU - Li, Yuqiang

AU - Dai, Hongshuai

PY - 2011/11

Y1 - 2011/11

N2 - Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.

AB - Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.

KW - Fractional Brownian motion

KW - Poisson process

KW - Weak convergence

UR - https://www.scopus.com/pages/publications/81455142035

U2 - 10.3150/10-BEJ319

DO - 10.3150/10-BEJ319

M3 - 文章

AN - SCOPUS:81455142035

SN - 1350-7265

VL - 17

SP - 1195

EP - 1216

JO - Bernoulli

JF - Bernoulli

IS - 4

ER -

Approximations of fractional Brownian motion

Abstract

Keywords

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