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A generalized backward scheme for solving nonmonotonic stochastic recursions. (English) Zbl 1318.60038
Summary: We propose an explicit construction of a stationary solution for a stochastic recursion of the form \(X\circ\theta=\varphi(X)\) on a partially-ordered Polish space, when the monotonicity of \(\varphi\) is not assumed. Under certain conditions, we show that an extension of the original probability space exists, on which a solution is well defined, and construct explicitly this extension using a randomized contraction technique. We then provide conditions for the existence of a solution on the original space. We finally apply these results to the stability study of two nonmonotonic queueing systems.

MSC:
60G10 Stationary stochastic processes
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K25 Queueing theory (aspects of probability theory)
37H99 Random dynamical systems
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