The Annals of Probability

Notes on the two-dimensional fractional Brownian motion

Fabrice Baudoin and David Nualart

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Abstract

We study the two-dimensional fractional Brownian motion with Hurst parameter H>½. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.

Article information

Source
Ann. Probab., Volume 34, Number 1 (2006), 159-180.

Dates
First available in Project Euclid: 17 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1140191535

Digital Object Identifier
doi:10.1214/009117905000000288

Mathematical Reviews number (MathSciNet)
MR2206345

Zentralblatt MATH identifier
1093.60016

Subjects
Primary: 60F15: Strong theorems 60G15: Gaussian processes 60G18: Self-similar processes 60H05: Stochastic integrals

Keywords
Ergodic theorem functionals of fractional Brownian motion planar fractional Brownian motion stochastic integrals windings

Citation

Baudoin, Fabrice; Nualart, David. Notes on the two-dimensional fractional Brownian motion. Ann. Probab. 34 (2006), no. 1, 159--180. doi:10.1214/009117905000000288. https://projecteuclid.org/euclid.aop/1140191535


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