An upper bound for the largest Lyapunov exponent of a Markovian product of nonnegative matrices

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Abstract

We derive an upper bound for the largest Lyapunov exponent of a Markovian product of nonnegative matrices using Markovian type counting arguments. The bound is expressed as the maximum of a nonlinear concave function over a finite-dimensional convex polytope of probability distributions.

Keywords

Entropy
Lyapunov exponent
Markov chains

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Research supported by ONR MURI N00014-1-0637, DARPA grant No. N66001-00-C-8062, and by NSF contract ECS 0123512.