Electronic Communications in Probability

Central limit theorem for an additive functional of the fractional Brownian motion II

David Nualart and Fangjun Xu

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Abstract

We prove a central limit theorem for an additivefunctional of the $d$-dimensional fractional Brownian motionwith Hurst index $H\in(\frac{1}{d+2},\frac{1}{d})$, using the method of moments,extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.

Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 74, 10 pp.

Dates
Accepted: 1 September 2013
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315613

Digital Object Identifier
doi:10.1214/ECP.v18-2761

Mathematical Reviews number (MathSciNet)
MR3101639

Zentralblatt MATH identifier
1329.60041

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G22: Fractional processes, including fractional Brownian motion

Keywords
ractional Brownian motion central limit theorem local time method of moments

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Nualart, David; Xu, Fangjun. Central limit theorem for an additive functional of the fractional Brownian motion II. Electron. Commun. Probab. 18 (2013), paper no. 74, 10 pp. doi:10.1214/ECP.v18-2761. https://projecteuclid.org/euclid.ecp/1465315613


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References

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  • Hu, Y.; Nualart, D. and Xu, F.: Central limit theorem for an additive functional of the fractional Brownian motion. Ann. Probab., accepted.
  • Papanicolaou, G. C.; Stroock, D.; Varadhan, S. R. S. Martingale approach to some limit theorems. Papers from the Duke Turbulence Conference (Duke Univ., Durham, N.C., 1976), Paper No. 6, ii+120 pp. Duke Univ. Math. Ser., Vol. III, Duke Univ., Durham, N.C., 1977.