Duffy, Ken and Dukes, W.M.B.
On Knuth’s Generalization of Banach’s Matchbox Problem.
Mathematical Proceedings of the Royal Irish Academy, 104A.
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.
||Knuth’s Generalization; Banach’s Matchbox Problem; Large Deviation Principle (LDP); stochastic process;
||Science & Engineering > Hamilton Institute
Dr Ken Duffy
||08 Oct 2010 15:16
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||Mathematical Proceedings of the Royal Irish Academy
||Royal Irish Academy
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