Open Access
January 1997 String matching bounds via coding
Paul C. Shields
Ann. Probab. 25(1): 329-336 (January 1997). DOI: 10.1214/aop/1024404290


It is known that the length $L(x_1^n)$ of the longest block appearing at least twice in a randomly chosen sample path of length $n$ drawn from an i.i.d. process is asymptotically almost surely equal to $C \log n$, where the constant $C$ depends on the process. A simple coding argument will be used to show that for a class of processes called the finite energy processes, $L(x_1^n)$ is almost surely upper bounded by $C \log n$, where $C$ is a constant. While the coding technique does not yield the exact constant $C$, it does show clearly what is needed to obtain log $n$ bounds.


Download Citation

Paul C. Shields. "String matching bounds via coding." Ann. Probab. 25 (1) 329 - 336, January 1997.


Published: January 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0873.60029
MathSciNet: MR1428511
Digital Object Identifier: 10.1214/aop/1024404290

Primary: 60G17
Secondary: 94A24

Keywords: prefix codes , string matching

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 1 • January 1997
Back to Top