A distribution F of a non-negative random variable belongs to the subexponential family of distributions S if 1-F’(2’)(x)∼2(1-F(x)) as x⇒•. This family is of considerable interest in branching processes, queueing theory, transient renewal theory and infinite divisibility theory. Much is known about the kind of distributions that belong to S but the question of whether S is closed under convolution has remained unresolved for some time. This paper contains an example which demonstrates that S is not in fact closed.
