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Large deviations theory : ウィキペディア英語版 | Large deviations theory In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. Some basic ideas of the theory can be traced back to Laplace and Cramér, but a clear and unified formal definition was only introduced in 1966, in a paper by Varadhan.〔S.R.S. Varadhan, ''Asymptotic probability and differential equations'', Comm. Pure Appl. Math. 19 (1966),261-286.〕 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. ==Introductory examples==
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