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On Knuth’s Generalization of Banach’s Matchbox Problem

Duffy, Ken and Dukes, W.M.B. (2004) On Knuth’s Generalization of Banach’s Matchbox Problem. Mathematical Proceedings of the Royal Irish Academy, 104A. pp. 107-118. ISSN 1393-7197

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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.

Item Type: Article
Keywords: Knuth’s Generalization; Banach’s Matchbox Problem; Large Deviation Principle (LDP); stochastic process;
Subjects: Science & Engineering > Hamilton Institute
Item ID: 2163
Depositing User: Dr Ken Duffy
Date Deposited: 08 Oct 2010 15:16
Journal or Publication Title: Mathematical Proceedings of the Royal Irish Academy
Publisher: Royal Irish Academy
Refereed: No
URI:

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