Varadhan's Lemma
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High Quality Content by WIKIPEDIA articles! In mathematics, Varadhan's lemma is a result in large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the asymptotic distribution of a statistic (Z ) of a family of random variables Z as becomes small in terms of a rate function for the variables. 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 tracked back to Laplace and Cramér, although a clear unified formal definition was…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, Varadhan's lemma is a result in large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the asymptotic distribution of a statistic (Z ) of a family of random variables Z as becomes small in terms of a rate function for the variables. 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 tracked back to Laplace and Cramér, although a clear unified formal definition was introduced in 1966 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 decay of the probability measures of certain kinds of extreme or tail events, as the number of observations grows arbitrarilylarge.