Large deviations for random walks under subexponentiality: the big-jump domain

Denisov, Denis, Dieker, A. B. and Shneer, V. 2008. Large deviations for random walks under subexponentiality: the big-jump domain. Annals of Probability 36 (5) , pp. 1946-1991. 10.1214/07-AOP382

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Abstract

For a given one-dimensional random walk {Sn} with a subexponential step-size distribution, we present a unifying theory to study the sequences {xn} for which as n→∞ uniformly for x≥xn. We also investigate the stronger “local” analogue, . Our theory is self-contained and fits well within classical results on domains of (partial) attraction and local limit theory. When specialized to the most important subclasses of subexponential distributions that have been studied in the literature, we reproduce known theorems and we supplement them with new results.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Large deviations; random walk; subexponentiality
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0091-1798/ (accessed 28/02/2014).
Publisher:	Institute of Mathematical Statistics
ISSN:	0091-1798
Date of First Compliant Deposit:	30 March 2016
Last Modified:	13 May 2023 12:44
URI:	https://orca.cardiff.ac.uk/id/eprint/13510

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