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

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  22 June 2017

Fangjun Xu
Fangjun Xu*
Affiliation:
East China Normal University and NYU Shanghai NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
*
* Postal address: School of Statistics, East China Normal University, Shanghai, 200241, China. Email address: fjxu@finance.ecnu.edu.cn
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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 motionshort-range dependencelimit lawmethod of moments

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G22: Fractional processes, including fractional Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 444 - 461
Copyright
Copyright © Applied Probability Trust 2017 

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References

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