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Quantitative bounds for large deviations of heavy tailed random variables (2202.02935v3)
Published 7 Feb 2022 in math.PR
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.