This article is cited in 9 papers

Cramer large deviations when the extreme conjugate distribution is heavy-tailed

A. V. Nagaev

Nikolaus Copernicus University

Abstract: The classical large deviations problem is considered under the assumption that the unilateral Cramer condition holds on a bounded interval. We assume that the extreme conjugate distribution is from the domain of attraction of a stable law. A limit is established up to which the asymptotic Cramer–Petrov representation is valid.

Keywords: conjugate distribution, slowly varying function, monotone $\varepsilon$-approximation.

Received: 05.11.1996

DOI: 10.4213/tvp1554

 English version: Theory of Probability and its Applications, 1999, 43:3, 405–421

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