A characterization of small and large time limit laws for self-normalized Lévy processes

Maller, Ross; Mason, David M

A characterization of small and large time limit laws for self-normalized Lévy processes

Date

2013

Authors

Maller, Ross

Mason, David M

Publisher

Springer

Abstract

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.

Keywords

Keywords: Domain of attraction; Large Times; Quadratic variations; Self-Normalized; Small Times; Stable laws; Number theory; Normal distribution Domain of Attraction of Normal Distribution; Large Times; Lévy Process; Quadratic Variation; Self-Normalized; Small Times; Stable Laws

URI

http://hdl.handle.net/1885/73765

Collections

ANU Research Publications

Type

Book chapter

Book Title

Limit Theorems in Probability, Statistics and Number Theory. Springer Proceedings in Mathematics and Statistics Volume 42

DOI

10.1007/978-3-642-36068-8_8

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A characterization of small and large time limit laws for self-normalized Lévy processes

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