Randomly Stopped Sums with Generalized Subexponential Distribution.

Let { ξ 1 , ξ 2 , ... } be a sequence of independent possibly differently distributed random variables, defined on a probability space (Ω , F , P) with distribution functions { F ξ 1 , F ξ 2 , ... } . Let η be a counting random variable independent of sequence { ξ 1 , ξ 2 , ... } . In this paper, we find conditions under which the distribution function of randomly stopped sum S η = ξ 1 + ξ 2 + ... + ξ η belongs to the class of generalized subexponential distributions. [ABSTRACT FROM AUTHOR]