Weighted power variations of iterated Brownian motion - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2008

Weighted power variations of iterated Brownian motion

Abstract

We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional distributions, and show that the laws of the limiting objects can always be expressed in terms of three independent Brownian motions X, Y and B, as well as of the local times of Y. In particular, our results involve ``weighted'' versions of Kesten and Spitzer's Brownian motion in random scenery. Our findings extend the theory initiated by Khoshnevisan and Lewis (1999), and should be compared with the recent result by Nourdin and Réveillac (2008), concerning the weighted power variations of fractional Brownian motion with Hurst index H=1/4.
Fichier principal
Vignette du fichier
IBM-versionfinale.pdf (290.32 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00185518 , version 1 (06-11-2007)
hal-00185518 , version 2 (14-06-2008)

Identifiers

Cite

Ivan Nourdin, Giovanni Peccati. Weighted power variations of iterated Brownian motion. 2008. ⟨hal-00185518v2⟩
173 View
283 Download

Altmetric

Share

Gmail Facebook X LinkedIn More