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.