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

Ross Maller; David M. Mason

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

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

Ross Maller, David M. Mason

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Citations (Scopus)

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.

Original language	English
Title of host publication	Limit Theorems in Probability, Statistics and Number Theory
Subtitle of host publication	In Honor of Friedrich Gotze
Publisher	Springer New York LLC
Pages	141-169
Number of pages	29
ISBN (Print)	9783642360671
DOIs	https://doi.org/10.1007/978-3-642-36068-8_8
Publication status	Published - 2013

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	42
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

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

Cite this

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title = "A characterization of small and large time limit laws for self-normalized L{\'e}vy process",

abstract = "We establish asymptotic distribution results for self-normalized L{\'e}vy processes at small and large times that are analogs of those of Chistyakov and G{\"o}tze [Ann. Probab. 32:28-77, 2004] for self-normalized sums.",

keywords = "Domain of Attraction of Normal Distribution, Large Times, L{\'e}vy Process, Quadratic Variation, Self-Normalized, Small Times, Stable Laws",

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A characterization of small and large time limit laws for self-normalized Lévy process. / Maller, Ross; Mason, David M.
Limit Theorems in Probability, Statistics and Number Theory: In Honor of Friedrich Gotze. Springer New York LLC, 2013. p. 141-169 (Springer Proceedings in Mathematics and Statistics; Vol. 42).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Maller, Ross

AU - Mason, David M.

PY - 2013

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N2 - 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.

AB - 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.

KW - Domain of Attraction of Normal Distribution

KW - Large Times

KW - Lévy Process

KW - Quadratic Variation

KW - Self-Normalized

KW - Small Times

KW - Stable Laws

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

M3 - Conference contribution

SN - 9783642360671

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SP - 141

EP - 169

BT - Limit Theorems in Probability, Statistics and Number Theory

PB - Springer New York LLC

ER -

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

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