Non-Improved Uniform Tail Estimates for Normed Sums of Independent Random Variables with Heavy Tails, with applications

Details Non-Improved Uniform Tail Estimates for Normed Sums of Independent Random Variables with Heavy Tails, with applications Non-Improved Uniform Tail Estimates for Normed Sums of Independent Random Variables with Heavy Tails, with applications

2011-10-21

arxiv.org/abs/1110.4879v1

Mathematics

Probability

Scientific paper

We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some applications in the method Monte-Carlo and statistics, and obtain the sufficient conditions for Central and stable limit theorem in the Banach space of continuous function. There are considered a slight generalization on a random variables with super-heavy tails and martingale difference scheme.

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