Weighted power variations of iterated Brownian motion

Ivan Nourdin, Giovanni Peccati
2008 Electronic Journal of Probability  
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
more » ... scenery. Our findings extend the theory initiated by , 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.
doi:10.1214/ejp.v13-534 fatcat:veensdaegbggxmbfttuvjzwzry