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February 2002 Large Deviations of Products of Random Topical Operators
Fergal Toomey
Ann. Appl. Probab. 12(1): 317-333 (February 2002). DOI: 10.1214/aoap/1015961166

Abstract

A topical operator on $\mathbb{R}^d$ is one which is isotone and homogeneous. Let ${A(n) : n \geq 1}$ be a sequence of i.i.d. random topical operators such that the projective radius of $A(n) \dots A(1)$ is almost surely bounded for large $n$. If ${x(n) : n \geq 1}$, is a sequence of vectors given by $x(n) = A(n) \dots A(1)x_0$, for some fixed initial condition $x_0$, then the sequence ${x(n)/n : n \geq 1}$ satisfies a weak large deviation principle. As corollaries of this result we obtain large deviation principles for products of certain random aperiodic max-plus and min-plus matrix operators and for products of certain random aperiodic nonnegative matrix operators.

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Fergal Toomey. "Large Deviations of Products of Random Topical Operators." Ann. Appl. Probab. 12 (1) 317 - 333, February 2002. https://doi.org/10.1214/aoap/1015961166

Information

Published: February 2002
First available in Project Euclid: 12 March 2002

zbMATH: 1073.60027
MathSciNet: MR1890067
Digital Object Identifier: 10.1214/aoap/1015961166

Subjects:
Primary: 60F10
Secondary: 47H07 , 47H40

Keywords: discrete event systems , large deviations , max-plus algebra , nonnegative matrices , Topical operators

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February 2002
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