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Some Ergodic Results on Stochastic Iterative Discrete Events Systems
Authors:Jean-Marc Vincent
Affiliation:(1) Laboratoire de Modèlisation et Calcul, Institut IMAG, BP 53, 38041 GRENOBLE Cedex, FRANCE
Abstract:This paper deals with the asymptotic behavior of the stochastic dynamics of discrete event systems. In this paper we focus on a wide class of models arising in several fields and particularly in computer science. This class of models may be characterized by stochastic recurrence equations in RopfK of the form T(n+1) = phgr n+1(T(n)) where phgr n is a random operator monotone and 1—linear. We establish that the behaviour of the extremas of the process T(n) are linear. The results are an application of the sub-additive ergodic theorem of Kingman. We also give some stability properties of such sequences and a simple method of estimating the limit points.
Keywords:Stochastic recurrence equations  performance evaluation  ergodicity  stability  subadditive ergodic theory
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