Quantitative bounds for large deviations of heavy tailed random variables
Probability
2024-02-15 v3
Abstract
The probability that the sum of independent, centered, identically distributed, heavy-tailed random variables achieves a very large value is asymptotically equal to the probability that there exists a single summand equalling that value. We quantify the error in this approximation. We furthermore characterise of the law of the individual summands, conditioned on the sum being large.
Cite
@article{arxiv.2202.02935,
title = {Quantitative bounds for large deviations of heavy tailed random variables},
author = {Quirin Vogel},
journal= {arXiv preprint arXiv:2202.02935},
year = {2024}
}
Comments
15 pages, fixed typos and extended to all alpha