Varadhan's Lemma is a result of large deviations theory that describes the asymptotic behavior of the expected value of an exponential functional of a family of random variables as a parameter controlling their fluctuations shrinks toward zero, expressing the limiting behavior in terms of the family's own large-deviations rate function. Named for S. R. Srinivasa Varadhan, it is a central tool for extracting asymptotic information about statistics of random variables once their large-deviations behavior is known.
Facts
StatementFor a family of random variables indexed by a shrinking parameter, the lemma gives the limiting asymptotic behavior of the expected value of an exponential functional of the family in terms of the family's own large deviations rate function. 1 Sources
1. Varadhan's lemma (Wikipedia)
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The result gives information on the asymptotic distribution of a statistic phi(Z_epsilon) of a family of random variables Z_epsilon as epsilon becomes small in terms of a rate function for the variables.
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