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2008 Weighted power variations of iterated Brownian motion
Ivan Nourdin, Giovanni Peccati
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Electron. J. Probab. 13: 1229-1256 (2008). DOI: 10.1214/EJP.v13-534


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 $H=1/4$.


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Ivan Nourdin. Giovanni Peccati. "Weighted power variations of iterated Brownian motion." Electron. J. Probab. 13 1229 - 1256, 2008.


Accepted: 3 August 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1193.60028
MathSciNet: MR2430706
Digital Object Identifier: 10.1214/EJP.v13-534

Primary: 60F05
Secondary: 60G18 , 60K37

Keywords: Brownian motion , Brownian motion in random scenery , iterated Brownian motion , limit theorems , Weighted power variations


Vol.13 • 2008
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