{"id":{"repo_id":"anu","oai_identifier":"oai:openresearch-repository.anu.edu.au:1885/12271"},"canonical_url":"https://search.dev.ndltd.org/etd/anu/oai:openresearch-repository.anu.edu.au:1885/12271","repository":{"repo_id":"anu","name":"Australian National University","base_url":"https://openresearch-repository.anu.edu.au/server/oai/request"},"display":{"title":"Small-time Chung Laws for L evy processes","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.","abstract_html":"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. 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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."]},{"key":"dc:title","label":"Title","values":["Small-time Chung Laws for L evy processes"]}]}],"canonical_facts":{"dc:creator":["Phelan, Thomas Michael"],"dc:date.accessioned":["2014-11-06T00:06:26Z"],"dc:date.available":["2014-11-06T00:06:26Z"],"dc:date.issued":["2014"],"dc:description.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."],"dc:identifier.other":["b36002355"],"dc:identifier.uri":["http://hdl.handle.net/1885/12271"],"dc:language.iso":["en_AU"],"dc:subject":["Levy processes","laws of the iterated logarithm of Chung type"],"dc:title":["Small-time Chung Laws for L evy processes"],"dc:type":["Thesis (MPhil)"]},"updated_at":"2026-07-24T00:54:36Z"}