Large Deviations Of Sums Mainly Due To Just One Summand

Iosif Pinelis

Large Deviations Of Sums Mainly Due To Just One Summand

Probability 2021-10-29 v1

Authors: Iosif Pinelis

Abstract

We present a formalization of the well-known thesis that, in the case of independent identically distributed random variables $X_1,\dots,X_n$ with power-like tails of index $\alpha\in(0,2)$ , large deviations of the sum $X_1+\dots+X_n$ are primarily due to just one of the summands.

Keywords

large deviations iid random variables power-like tails sum of random variables

Cite

@article{arxiv.2110.14741,
  title  = {Large Deviations Of Sums Mainly Due To Just One Summand},
  author = {Iosif Pinelis},
  journal= {arXiv preprint arXiv:2110.14741},
  year   = {2021}
}

Comments

6 pages; to appear in The American Mathematical Monthly

Related papers

View all related →