Second-order limit laws for occupation times of fractional Brownian motion

Fangjun Xu

doi:10.1017/jpr.2017.10

Second-order limit laws for occupation times of fractional Brownian motion

Fangjun Xu^*

^*Corresponding author for this work

School of Statistics

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

3 Scopus citations

Abstract

We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1/d, using the method of moments and extending the Kallianpur-Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

Original language	English
Pages (from-to)	444-461
Number of pages	18
Journal	Journal of Applied Probability
Volume	54
Issue number	2
DOIs	https://doi.org/10.1017/jpr.2017.10
State	Published - 1 Jun 2017

Keywords

Fractional Brownian motion
limit law
method of moments
short-range dependence

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10.1017/jpr.2017.10

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title = "Second-order limit laws for occupation times of fractional Brownian motion",

abstract = "We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1/d, using the method of moments and extending the Kallianpur-Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.",

keywords = "Fractional Brownian motion, limit law, method of moments, short-range dependence",

author = "Fangjun Xu",

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year = "2017",

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doi = "10.1017/jpr.2017.10",

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AU - Xu, Fangjun

PY - 2017/6/1

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N2 - We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1/d, using the method of moments and extending the Kallianpur-Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

AB - We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1/d, using the method of moments and extending the Kallianpur-Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

KW - Fractional Brownian motion

KW - limit law

KW - method of moments

KW - short-range dependence

UR - https://www.scopus.com/pages/publications/85021099216

U2 - 10.1017/jpr.2017.10

DO - 10.1017/jpr.2017.10

M3 - 文章

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SN - 0021-9002

VL - 54

SP - 444

EP - 461

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 2

ER -

Second-order limit laws for occupation times of fractional Brownian motion

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Keywords

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