Abstract
In this paper the asymptotic growth rate of stochastic max-plus linear systems is studied. For non-random irreducible max-plus linear systems the existence of this growth rate is well known. For stochastic systems conditions for the existence of the growth rate will be developed. The conditions are mild and natural, and weaker than the conditions used in literature until now. The interpretation of the conditions is that for the asymptotic growth rate to exist the stochastic max-plus linear system should be dominated from below by a non-random irreducible max-plus linear system. The latter condition need not to be true always, but should at least hold with some positive probability. The investigations in this paper are motivated by means of some examples.
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