Regularly distributed randomly stopped sum, minimum, and maximum

Abstract

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