This article is cited in 3 papers

On large deviations, I

S. V. Zhulenev

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

Abstract: A new point of view is suggested on the Cramér idea, which celebrated its 60th anniversary in 1998: to use a measure transform to obtain the so-called representation of large deviation type. This slightly different approach allows us to understand that the old idea is more efficient than had been thought before, even in the one-dimensional case.

Keywords: generalized Cramér transform, independent nonidentically distributed summands, nonasymptotic large deviation problem.

Received: 01.07.1997

DOI: 10.4213/tvp596

 English version: Theory of Probability and its Applications, 2000, 44:1, 75–92

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