Exact Asymptotics for Large Deviation Probabilities, with Applications

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.

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