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 AbstractWe 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. | Keywords: | Knuth’s Generalization; Banach’s Matchbox Problem; Large Deviation Principle (LDP); stochastic process; |
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| Subjects: | Science & Engineering > Hamilton Institute |
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| ID Code: | 2163 |
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| Deposited By: | Dr Ken Duffy |
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| Deposited On: | 08 Oct 2010 16:16 |
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| Journal or Publication Title: | Mathematical Proceedings of the Royal Irish Academy |
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| Publisher: | Royal Irish Academy |
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| Refereed: | No |
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