A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$

Details A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$ A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$

2008-08-26

arxiv.org/abs/0808.3458v2

Mathematics

Probability

70 pages, 1 figure

Scientific paper

Let $B=(B^{(1)},B^{(2)})$ be a two-dimensional fractional Brownian motion with Hurst index $\alpha\in (0,1/4)$. Using an analytic approximation $B(\eta)$ of $B$ introduced in \cite{Unt08}, we prove that the rescaled L\'evy area process $(s,t)\to \eta^{\half(1-4\alpha)}\int_s^t dB_{t_1}^{(1)}(\eta) \int_s^{t_1} dB_{t_2}^{(2)}(\eta)$ converges in law to $W_t-W_s$ where $W$ is a Brownian motion independent from $B$. The method relies on a very general scheme of analysis of singularities of analytic functions, applied to the moments of finite-dimensional distributions of the L\'evy area.

Affiliated with

Also associated with

No associations

Rating

A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-281237