Weighted power variations of iterated Brownian motion

Details Weighted power variations of iterated Brownian motion Weighted power variations of iterated Brownian motion

2007-11-06

arxiv.org/abs/0711.0858v2

Mathematics

Probability

27 pages

Scientific paper

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 R\'eveillac (2008), concerning the weighted power variations of fractional Brownian motion with Hurst index H=1/4.

Affiliated with

Also associated with

No associations

Rating

Weighted power variations of iterated Brownian motion 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 Weighted power variations of iterated Brownian motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weighted power variations of iterated Brownian motion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-134417