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Appl Applied Probability Trust approximation assume assumption barrier boundary branching process central limit central limit theorem coefficients consider constant convergence Corollary defined denote distribution function elements ergodic estimates exponential exponential distribution finite follows Galton-Watson process Gani Gaussian given Hannan hence identity implies independent infectives infinite infinity input process integral interval invariant measure lattice Lemma lim sup limit theorem limiting distribution linear Markov chain Markov processes Markov system Markovian Math Mathematical matrix mean non-negative normal distribution obtain optimal order pairs P-class paper points Poisson positive Printed in Israel Prob probability generating function probability measure Probability Trust 1973 Proof of Theorem properties prove queue random variables random walk Received in revised recurrent result satisfies Section sequence solution space Statist stochastic epidemic Stochastic Processes Suppose theory transition University values variance vector Whittle yields zero