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Duffy, Ken R. 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; |
| Academic Unit: | Faculty of Science and Engineering > Research Institutes > 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: | https://mural.maynoothuniversity.ie/id/eprint/2163 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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