LARGE DEVIATIONS OF MEANS OF HEAVY-TAILED RANDOM VARIABLES WITH FINITE MOMENTS OF ALL ORDERS

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Lehtomaa , J 2017 , ' LARGE DEVIATIONS OF MEANS OF HEAVY-TAILED RANDOM VARIABLES WITH FINITE MOMENTS OF ALL ORDERS ' , Journal of Applied Probability , vol. 54 , no. 1 , pp. 66-81 . https://doi.org/10.1017/jpr.2016.87

Title: LARGE DEVIATIONS OF MEANS OF HEAVY-TAILED RANDOM VARIABLES WITH FINITE MOMENTS OF ALL ORDERS
Author: Lehtomaa, Jaakko
Contributor organization: Department of Mathematics and Statistics
Date: 2017-03
Language: eng
Number of pages: 16
Belongs to series: Journal of Applied Probability
ISSN: 0021-9002
DOI: https://doi.org/10.1017/jpr.2016.87
URI: http://hdl.handle.net/10138/308459
Abstract: Logarithmic asymptotics of the mean process {S-n/n} are investigated in the presence of heavy-tailed increments. As a consequence, a full large deviations principle for means is obtained when the hazard function of an increment is regularly varying with index alpha epsilon (0, 1). This class includes all stretched exponential distributions. Thus, the previous research of Gantert et al. (2014) is extended. Furthermore, the presented proofs are more transparent than the techniques used by Nagaev (1979). In addition, the novel approach is compatible with other common classes of distributions, e. g. those of lognormal type.
Subject: Logarithmic asymptotics
regular variation
stretched exponential
large deviation
heavy-tailed
PRINCIPLE
SUMS
111 Mathematics
Peer reviewed: Yes
Rights: cc_by_nc_nd
Usage restriction: openAccess
Self-archived version: acceptedVersion


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