Regularly distributed randomly stopped sum, minimum, and maximum - Sprindys, Jonas; Šiaulys, Jonas (Nonlinear Analysis: Modelling and Control, 2020)
Let {ξ1,ξ2,...} be a sequence of independent real-valued, possibly nonidentically distributed, random variables, and let η be a nonnegative, nondegenerate at 0, and integer-valued random variable, which is independent of {ξ1,ξ2,...}. We consider conditions for {ξ1,ξ2,...} and η under which the distributions of the randomly stopped minimum, maximum, and sum are regularly varying.
Keywords: regularly varying distribution; counting random variable; randomly stopped maximum; randomly stopped minimum; randomly stopped sum; closure property