This article is cited in 1 paper

On large deviations, II

S. V. Zhulenev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The Esscher–Cramér approach enables us to get representations of large deviation type even if the Cramér condition fails. Moreover, in the case of the scaled sums of a sequence of independent identically distributed random variables these representations turn out to be slightly different from those which are correct under this rigid condition.

Keywords: generalized Cramér transform, truncated exponential, conditional expectations.

Received: 18.07.2001

DOI: 10.4213/tvp188

 English version: Theory of Probability and its Applications, 2005, 49:4, 671–690

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