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On Knuth's generalization of Banach's matchbox problem

Dukes, W.M.B. and Duffy, Ken (2004) On Knuth's generalization of Banach's matchbox problem. Mathematical Proceedings of the Royal Irish Academy, 104 (1). pp. 107-118.

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Abstract

We revisit a simply stated problem of Knuth. Previous approaches rely on the Bernoulli nature of the underlying stochastic process to recover the systems mean behaviour. We show that limiting results hold for a wide range of stochastic processes. A Large Deviation Principle (LDP) is proved, allowing estimates to be made for the probability of rare-events. From the LDP, a weak law of large numbers is deduced.