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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 43 open journal systems 


Weighted power variations of iterated Brownian motion

Ivan Nourdin, Université Paris 6
Giovanni Peccati, Université Paris 6


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.


Full text: PDF

Pages: 1229-1256

Published on: August 3, 2008
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Electronic Journal of Probability. ISSN: 1083-6489