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Thick Points for Transient Symmetric Stable Processes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Thick Points for Transient Symmetric Stable Processes
2.	Creator	Author's name, affiliation, country	Amir Dembo; Stanford University
2.	Creator	Author's name, affiliation, country	Yuval Peres; University of California, Berkeley
2.	Creator	Author's name, affiliation, country	Jay Rosen; College of Staten Island, CUNY
2.	Creator	Author's name, affiliation, country	Ofer Zeitouni; Technion
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	Stable process, occupation measure, multifractal spectrum.
3.	Subject	Subject classification	60J55.
4.	Description	Abstract	Let $T(x,r)$ denote the total occupation measure of the ball of radius $r$ centered at $x$ for a transient symmetric stable processes of index $b<d$ in $R^d$ and $K(b,d)$ denote the norm of the convolution with its 0-potential density, considered as an operator on $L^2(B(0,1),dx)$. We prove that as $r$ approaches 0, almost surely $\sup_{|x| \leq 1} T(x,r)/(r^b|\log r|) \to b K(b,d)$. Furthermore, for any $a \in (0,b/K(b,d))$, the Hausdorff dimension of the set of ``thick points'' $x$ for which $\limsup_{r \to 0} T(x,r)/(r^b |\log r|)=a$, is almost surely $b-a/K(b,d)$; this is the correct scaling to obtain a nondegenerate ``multifractal spectrum'' for transient stable occupation measure. The liminf scaling of $T(x,r)$ is quite different: we exhibit positive, finite, non-random $c(b,d), C(b,d)$, such that almost surely $c(b,d)<\sup_x \liminf_{r \to 0} T(x,r)/r^b<C(b,d)$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1999-05-05
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/47
10.	Identifier	Digital Object Identifier	10.1214/EJP.v4-47
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 4
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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