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2018nagaev-revised.pdf
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Final Accepted Manuscript
Affiliation
Univ Arizona, Dept MathIssue Date
2019-03Keywords
Local limit lawsLarge deviations
Heavy-tailed random variables
Asymptotic analysis
Lindelof integral
Singularity analysis
Bivariate steepest descent
Metadata
Show full item recordPublisher
SPRINGER/PLENUM PUBLISHERSCitation
Ercolani, N.M., Jansen, S. & Ueltschi, D. J Theor Probab (2019) 32: 1. https://doi.org/10.1007/s10959-018-0832-2Rights
© Springer Science+Business Media, LLC, part of Springer Nature 2018.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We propose a novel complex-analytic method for sums of i.i.d. random variables that are heavy-tailed and integer-valued. The method combines singularity analysis, Lindelof integrals, and bivariate saddle points. As an application, we prove three theorems on precise large and moderate deviations which provide a local variant of a result by Nagaev (Transactions of the sixth Prague conference on information theory, statistical decision functions, random processes, Academia, Prague, 1973). The theorems generalize five theorems by Nagaev (Litov Mat Sb 8:553-579, 1968) on stretched exponential laws p(k)=cexp(-k) and apply to logarithmic hazard functions cexp(-(logk)), >2; they cover the big-jump domain as well as the small steps domain. The analytic proof is complemented by clear probabilistic heuristics. Critical sequences are determined with a non-convex variational problem.Note
12 month embargo; published online: 26 May 2018ISSN
0894-98401572-9230
Version
Final accepted manuscriptSponsors
NSF [DMS-1212167]Additional Links
http://link.springer.com/10.1007/s10959-018-0832-2ae974a485f413a2113503eed53cd6c53
10.1007/s10959-018-0832-2