Central limit theorem for an additive functional of the fractional brownian motion

Yaozhong Hu; David Nualart; Fangjun Xu

doi:10.1214/12-AOP825

Central limit theorem for an additive functional of the fractional brownian motion

Yaozhong Hu
, David Nualart
, Fangjun Xu

School of Statistics

University of Kansas

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

15 Scopus citations

Abstract

We prove a central limit theorem for an additive functional of the ddimensional fractional Brownian motion with Hurst index H ε ( 1/1+d, 1/d ), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.

Original language	English
Pages (from-to)	168-203
Number of pages	36
Journal	Annals of Probability
Volume	42
Issue number	1
DOIs	https://doi.org/10.1214/12-AOP825
State	Published - Jan 2014

Keywords

Central limit theorem
Fractional brownian motion
Local time
Method of moments

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10.1214/12-AOP825

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title = "Central limit theorem for an additive functional of the fractional brownian motion",

abstract = "We prove a central limit theorem for an additive functional of the ddimensional fractional Brownian motion with Hurst index H ε ( 1/1+d, 1/d ), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.",

keywords = "Central limit theorem, Fractional brownian motion, Local time, Method of moments",

author = "Yaozhong Hu and David Nualart and Fangjun Xu",

year = "2014",

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doi = "10.1214/12-AOP825",

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AU - Nualart, David

AU - Xu, Fangjun

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N2 - We prove a central limit theorem for an additive functional of the ddimensional fractional Brownian motion with Hurst index H ε ( 1/1+d, 1/d ), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.

AB - We prove a central limit theorem for an additive functional of the ddimensional fractional Brownian motion with Hurst index H ε ( 1/1+d, 1/d ), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.

KW - Central limit theorem

KW - Fractional brownian motion

KW - Local time

KW - Method of moments

UR - https://www.scopus.com/pages/publications/84893176238

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DO - 10.1214/12-AOP825

M3 - 文章

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SN - 0091-1798

VL - 42

SP - 168

EP - 203

JO - Annals of Probability

JF - Annals of Probability

IS - 1

ER -

Central limit theorem for an additive functional of the fractional brownian motion

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Keywords

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