Abstract
IN many applications of the theory of stochastic processes to, for example, epidemics, storage, queues, reliability and risk theory, the mathematical model that often emerges is governed by a skip free Markov chain or process which is basically very simple and is complicated only by the presence of boundaries. (A process is said to be skip free if its states are strictly ordered and passage from one particular state can only take place to its neighbouring states.) Frequently the underlying process is skip free in at least one direction. I shall describe a method for dealing with such situations and relate the discussion to a model for a finite dam in discrete time and with a discrete state space. The basic ideas have also been applied to a situation in which time and state space are continuous1,2.
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