Extreme value theory for a class of discrete distributions with applications to some stochastic processes

Let ξ n be the maximum of a set of n independent random variables with common distribution function F whose support consists of all sufficiently large positive integers. Some of the classical asymptotic results of extreme value theory fail to apply to ξ n for such F and this paper attempts to find weaker ones which give some description of the behaviour of ξ n as n → ∞. These are then applied to the extreme value theory of certain regenerative stochastic processes.