Large deviations theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Large_deviations_theory


00:00:50 1 Introductory examples
00:01:00 1.1 An elementary example
00:06:44 1.2 Large deviations for sums of independent random variables
00:11:07 2 Formal definition
00:14:45 3 Brief history
00:16:41 4 Applications
00:17:16 4.1 Large deviations and entropy
00:19:30 5 See also



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SUMMARY
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In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the theory can be traced to Laplace, the formalization started with insurance mathematics, namely ruin theory with  Cramér and Lundberg. A unified formalization of large deviation theory was developed in 1966, in a paper by Varadhan. Large deviations theory formalizes the heuristic ideas of concentration of measures and widely generalizes the notion of convergence of probability measures.
Roughly speaking, large deviations theory concerns itself with the exponential decline of the probability measures of certain kinds of extreme or tail events.