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Stationary distributions for fluid flow models with or without Brownian noise. (English) Zbl 0817.60086
One considers a stochastic process with reflection at the origin and paths which are piecewise linear or Brownian, with the drift and variance constants being determined by the state of an underlying finite Markov process. It is shown that the stationary distribution is phase-type, and some computing algorithms are proposed. The paper refers to time-reversal Markov processes, Wiener-Hopf factorization and nonlinear iteration.

MSC:
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60K15 Markov renewal processes, semi-Markov processes
60J05 Discrete-time Markov processes on general state spaces
47D07 Markov semigroups and applications to diffusion processes
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