Small-time Chung Laws for L evy processes
type: CreativeWork
description: In this thesis we review and add to the literature extending the so-called `other' law of the iterated logarithm of Chung (1948). By adapting the large-time techniques of Rushton (2007) to the small-time setting and employing and slightly extending a characterisation result of Maller and Mason (2008), we derive both one-dimensional and functional Chung laws for a large class of Levy processes lying in the domain of attraction of strictly stable laws at zero. In particular, our results extend the work of Buchmann and Maller (2011) to encompass processes with vanishing Gaussian component lying in the domain of attraction of a normal distribution at zero.
abstract: In this thesis we review and add to the literature extending the so-called `other' law of the iterated logarithm of Chung (1948). By adapting the large-time techniques of Rushton (2007) to the small-time setting and employing and slightly extending a characterisation result of Maller and Mason (2008), we derive both one-dimensional and functional Chung laws for a large class of Levy processes lying in the domain of attraction of strictly stable laws at zero. In particular, our results extend the work of Buchmann and Maller (2011) to encompass processes with vanishing Gaussian component lying in the domain of attraction of a normal distribution at zero.
author: Phelan, Thomas Michael
language: en_AU
keywords: Levy processes, laws of the iterated logarithm of Chung type
date published: 2014
date modified: 2026-07-24T01:07:16Z
provider: Australian Catholic University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Australian Catholic University

PropertyValue
property ID: Handle
value: http://hdl.handle.net/1885/12271