A Characterization of Small and Large Time Limit Laws for Self-normalized Lévy Processes
We establish asymptotic distribution results for self-normalized Lévy processes at small and large times that are analogs of those of Chistyakov and Götze [Ann. Probab. 32:28–77, 2004] for self-normalized sums.
KeywordsDomain of Attraction of Normal Distribution Large Times Lévy Process Quadratic Variation Self-Normalized Small Times Stable Laws
Research of Ross Maller was partially supported by ARC Grant DP1092502. Research of David M. Mason was partially supported by NSF Grant DMS–0503908.
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