Lower bounds of the Hausdorff dimension for the images of Feller processes

V. Knopova, R.L. Schilling and J. Wang

Statistics & Probability Letters, 2015, vol. 97, issue C, 222-228

Abstract: Let (Xt)t⩾0 be a Feller process generated by a pseudo-differential operator whose symbol satisfies ‖p(⋅,ξ)‖∞⩽c(1+|ξ|2) and p(⋅,0)≡0. We prove that, for a large class of examples, the Hausdorff dimension of the set {Xt:t∈E} for any analytic set E⊂[0,∞) is almost surely bounded below by δ∞dimHE, whereδ∞≔sup{δ>0:lim|ξ|→∞infz∈RdRep(z,ξ)|ξ|δ=∞}. This, along with the upper bound β∞dimHE with β∞≔inf{δ>0:lim|ξ|→∞sup|η|⩽|ξ|supz∈Rd|p(z,η)||ξ|δ=0} established in Böttcher, Schilling and Wang (2014), extends the dimension estimates for Lévy processes of Blumenthal and Getoor (1961) and Millar (1971) to Feller processes.

Keywords: Feller process; Pseudo-differential operator; Symbol; Hausdorff dimension; Blumenthal–Getoor index (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715214004039
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:stapro:v:97:y:2015:i:c:p:222-228

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

DOI: 10.1016/j.spl.2014.11.027

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().