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.
Publié le : 2002-02-14
Classification:
Topical operators,
discrete event systems,
max-plus algebra,
nonnegative matrices,
large deviations,
60F10,
47H40,
47H07
@article{1015961166,
author = {Toomey, Fergal},
title = {Large Deviations of Products of Random Topical Operators},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 317-333},
language = {en},
url = {http://dml.mathdoc.fr/item/1015961166}
}
Toomey, Fergal. Large Deviations of Products of Random Topical Operators. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 317-333. http://gdmltest.u-ga.fr/item/1015961166/