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

D.E. Denisov, A.B. Dieker, V. Shneer

Research output: Contribution to journalArticleAcademicpeer-review

107 Citations (Scopus)
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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¿8 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.
Original languageEnglish
Pages (from-to)1946-1991
JournalThe Annals of Probability
Volume36
Issue number5
DOIs
Publication statusPublished - 2008

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