Title: Closure properties for heavy-tailed distributions: Some recent results
Authors: Remigijus Leipus - Vilnius University (Lithuania) [presenting]
Abstract: The aim is to give a short overview of closure properties for heavy-tailed and related distributions, covering regularly, consistently varying, subexponential, long-tailed and other distributions. Recall that the closure property states that, assuming that two or more distributions are in some specific class, their transformation belongs to the same class of distributions. The main attention is focused to the sum-, mixture, min-, max- and power-convolution closure properties. Additionally, we present some recent results on random sum- and random max-closure properties for dependent and nonidentically distributed heavy-tailed random variables.