Difference between revisions of "Talk:Probability of large deviations"
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Nowadays large deviations are usually understood as ''logarithmic'' asymptotics of small probabilities in the region where the normal approximation fails even on the logarithmic level. The theory is formulated in terms of rate functions; terribly, rate function is not mentioned at all in our encyclopedia! The more narrow region where probabilities are small but the normal approximation holds on the logarithmic level is well-known as ''moderate deviations'' (only mentioned twice in our encyclopedia: in "[[Wiener sausage]]" and "[[Intermediate efficiency]]". | Nowadays large deviations are usually understood as ''logarithmic'' asymptotics of small probabilities in the region where the normal approximation fails even on the logarithmic level. The theory is formulated in terms of rate functions; terribly, rate function is not mentioned at all in our encyclopedia! The more narrow region where probabilities are small but the normal approximation holds on the logarithmic level is well-known as ''moderate deviations'' (only mentioned twice in our encyclopedia: in "[[Wiener sausage]]" and "[[Intermediate efficiency]]". | ||
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By the way, Srinivasa S. R. Varadhan was awarded the Abel Prize (2007) "for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations". | By the way, Srinivasa S. R. Varadhan was awarded the Abel Prize (2007) "for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations". | ||
--[[User:Boris Tsirelson|Boris Tsirelson]] 16:51, 25 April 2012 (CEST) | --[[User:Boris Tsirelson|Boris Tsirelson]] 16:51, 25 April 2012 (CEST) | ||
Latest revision as of 19:09, 25 April 2012
The article is quite obsolete, as is noted in its "Comments" section. Some literature is given in that section, but a number of more recent books should be used, too.
Nowadays large deviations are usually understood as logarithmic asymptotics of small probabilities in the region where the normal approximation fails even on the logarithmic level. The theory is formulated in terms of rate functions; terribly, rate function is not mentioned at all in our encyclopedia! The more narrow region where probabilities are small but the normal approximation holds on the logarithmic level is well-known as moderate deviations (only mentioned twice in our encyclopedia: in "Wiener sausage" and "Intermediate efficiency".
Thus, a complete rewrite is desirable.
By the way, Srinivasa S. R. Varadhan was awarded the Abel Prize (2007) "for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations".
--Boris Tsirelson 16:51, 25 April 2012 (CEST)
Probability of large deviations. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Probability_of_large_deviations&oldid=25394