Hausdorff Measure for a Stable-Like Process over an Infinite Extension of a Local Field

Anatoly N. Kochubei ()
Additional contact information
Anatoly N. Kochubei: Institute of Mathematics

Journal of Theoretical Probability, 2002, vol. 15, issue 4, 951-972

Abstract: Abstract We consider an infinite extension K of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. K is equipped with an inductive limit topology; its conjugate K is a completion of K with respect to a topology given by certain explicitly written seminorms. The semigroup of measures, which defines a stable-like process X(t) on K, is concentrated on a compact subgroup S ⊂ K. We study properties of the process X S (t), a part of X(t) in S. It is shown that the Hausdorff and packing dimensions of the image of an interval equal 0 almost surely. In the case of tamely ramified extensions a correct Hausdorff measure for this set is found.

Keywords: Stable process; local field; tamely ramified extension; Hausdorff dimension; Hausdorff measure (search for similar items in EconPapers)
Date: 2002
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1020789821275 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jotpro:v:15:y:2002:i:4:d:10.1023_a:1020789821275

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1020789821275

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().