We study asymptotic properties of non-negative random variables Xn, n[greater-or-equal, slanted]0, satisfying the recursion . If the functions g(x) and [sigma]2(x) are properly balanced at infinity, Xn is asymptotically [Gamma]-distributed in a suitable scale. This result contains several known...

Let {Zn} be a supercritical Galton-Watson process in varying environments. It is known that Zn when normed by its mean EZn converges almost surely to a finite random variable W. It is possible, however, for such a process to exhibit more than one rate of growth so that in particular {W 0} need...

It is known that, subject to some technical conditions, the deficit process of an infinitely deep dam with a Markov chain input process and unit withdrawals has a limiting zero-modified geometric distribution. In this paper it is shown that, provided the state space of the input process is...