Poisson Calculus and Queues
The phrase Poisson system is an abbreviation of dynamical system driven by Poisson processes. Poisson systems form a special class of the so-called stochastic discrete-event dynamical systems. Their dynamics are expressed in a manner quite analogous in spirit to the recurrence equation of a discrete-time HMC, Theorem 2.1, Chapter 2. However, for Poisson systems, the white noise is a family of independent Poisson processes, and the functional, which associates to the present value of the state process and to the present value of the noise the future value of the state process, does not have —in general— a closed expression but takes the form of an algorithm.
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