Recurrent lines in two-parameter isotropic stable Lévy sheets

Robert C. Dalang and Davar Khoshnevisan

Stochastic Processes and their Applications, 2004, vol. 114, issue 1, 81-107

Abstract: It is well known that an -valued isotropic [alpha]-stable Lévy process is (neighborhood-)recurrent if and only if d[less-than-or-equals, slant][alpha]. Given an -valued two-parameter isotropic [alpha]-stable Lévy sheet {X(s,t)}s,t[greater-or-equal, slanted]0, this is equivalent to saying that for any fixed s[set membership, variant][1,2], P{t|->X(s,t) is recurrent}=0 if d>[alpha] and =1 otherwise. We prove here that P{[there exists]s[set membership, variant][1,2]: t|->X(s,t) is recurrent}=0 if d>2[alpha] and =1 otherwise. Moreover, for d[set membership, variant]([alpha],2[alpha]], the collection of all times s at which t|->X(s,t) is recurrent is a random set of Hausdorff dimension 2-d/[alpha] that is dense in , a.s. When [alpha]=2, X is the two-parameter Brownian sheet, and our results extend those of Fukushima and Kôno.

Keywords: Stable; sheets; Recurrence (search for similar items in EconPapers)
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(04)00090-0
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:114:y:2004:i:1:p:81-107

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().