On Knuth's generalization of Banach's matchbox problem

W.M.B. Dukes; Ken Duffy

On Knuth's generalization of Banach's matchbox problem

W.M.B. Dukes
, Ken Duffy

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	107-118
Number of pages	12
Journal	Mathematical Proceedings of the Royal Irish Academy
Volume	104
Issue number	1
Publication status	Published - Nov 2004

Keywords

Knuth
Banach's matchbox problem
large deviation principles

Cite this

@article{70bd1c5a8b2d4eb59d3342c20e4437b6,

title = "On Knuth's generalization of Banach's matchbox problem",

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.",

keywords = "Knuth, Banach's matchbox problem, large deviation principles",

author = "W.M.B. Dukes and Ken Duffy",

year = "2004",

month = nov,

language = "English",

volume = "104",

pages = "107--118",

journal = "Mathematical Proceedings of the Royal Irish Academy",

issn = "2009-0021",

publisher = "Royal Irish Academy",

number = "1",

}

TY - JOUR

T1 - On Knuth's generalization of Banach's matchbox problem

AU - Dukes, W.M.B.

AU - Duffy, Ken

PY - 2004/11

Y1 - 2004/11

N2 - 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.

AB - 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.

KW - Knuth

KW - Banach's matchbox problem

KW - large deviation principles

UR - http://www.jstor.org/stable/40656874

M3 - Article

SN - 2009-0021

VL - 104

SP - 107

EP - 118

JO - Mathematical Proceedings of the Royal Irish Academy

JF - Mathematical Proceedings of the Royal Irish Academy

IS - 1

ER -

On Knuth's generalization of Banach's matchbox problem

Abstract

Keywords

Other files and links

Fingerprint

Cite this