# On the probability of large deviations in Banach spaces

Bolthausen, E (1984). On the probability of large deviations in Banach spaces. The Annals of Probability, 12(2):427-435.

## Abstract

Probabilities of large deviations for sums of i.i.d. Banach space valued random variables are investigated when the laws of the random variables converge weakly and a uniform exponential integrability condition is satisfied. Furthermore, a discussion of possible improvements of the estimates is given, when the probability is estimated that the sum lies in a convex set.

## Abstract

Probabilities of large deviations for sums of i.i.d. Banach space valued random variables are investigated when the laws of the random variables converge weakly and a uniform exponential integrability condition is satisfied. Furthermore, a discussion of possible improvements of the estimates is given, when the probability is estimated that the sum lies in a convex set.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Banach space valued random variables, large deviations English 1984 19 Oct 2009 12:20 24 Sep 2019 16:20 Institute of Mathematical Statistics 0091-1798 Green https://doi.org/10.1214/aop/1176993298 http://www.zentralblatt-math.org/zmath/en/search/?q=an:0538.60008

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