Journal ArticleDOI
Probabilities of large deviations for sums of random vectors
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This article is published in Lithuanian Mathematical Journal.The article was published on 1981-04-01. It has received 4 citations till now. The article focuses on the topics: Large deviations theory & Ordinary differential equation.read more
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Book ChapterDOI
Limit Theorems on Large Deviations
L. Saulis,V. Statulevičius +1 more
TL;DR: In this paper, the authors deal with limit theorems on large deviations on independent random variables and apply analytic tools that are applicable to this case that allow one to understand the general behavior of the probabilities of large deviations.
Journal ArticleDOI
Abelian theorems, limit properties of conjugate distributions, and large deviations for sums of independent random vectors ∗
TL;DR: In this paper, the authors considered a class of multidimensional absolutely continuous distributions, where each distribution has a moment generating function, which is finite in a bounded convex set S and generates a family of the so-called conjugate distributions.
References
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Book
Limit Distributions for Sums of Independent Random Variables
B. W. Gnedenko,A. N. Kolmogorov +1 more
Book
Normal Approximation and Asymptotic Expansions
Rabi Bhattacharya,R. Ranga Rao +1 more
TL;DR: In this paper, the Euler-MacLaurin sum formula for functions of several variables has been applied to the problem of convergence of probability measures and uniformity classes, and it has been shown that it is possible to obtain strong convergence for continuous, singular, and discrete probability measures.
Journal ArticleDOI