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
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.
Repository Staff Only: item control page