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Weighted power variations of iterated Brownian motion


 
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1. Title Title of document Weighted power variations of iterated Brownian motion
 
2. Creator Author's name, affiliation, country Ivan Nourdin; Université Paris 6
 
2. Creator Author's name, affiliation, country Giovanni Peccati; Université Paris 6
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian motion; Brownian motion in random scenery; Iterated Brownian motion; Limit theorems; Weighted power variations
 
3. Subject Subject classification 60F05; 60G18; 60K37
 
4. Description 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 $H=1/4$.
 
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7. Date (YYYY-MM-DD) 2008-08-03
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/534
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-534
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
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