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Exact Asymptotics for Large Deviation Probabilities, with Applications

  • Iosif Pinelis
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 46)

Abstrac

Three related groups of problems are surveyed, all of which concern asymptotics of large deviation probabilities themselves — rather than the much more commonly considered asymptotics of the logarithm of such probabilities. The former kind of asymptotics is sometimes referred to as “exact”, while the latter as “rough”. Obviously, “exact” asymptotics statements provide more information; the tradeoff is that additional restrictions on regularity of underlying probability distributions and/or on the corresponding zone of deviations are then required.

Keywords

large deviation probabilities final zero crossing last negative sum last positive sum nonparametric bandit theory subexponential distributions superexponential distributions exponential probabilistic inequalities 

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Copyright information

© Springer Science + Business Media, Inc. 2002

Authors and Affiliations

  • Iosif Pinelis
    • 1
  1. 1.Department of Mathematical SciencesMichigan Technological UniversityHoughton

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