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Finding transient solutions in Markovian event systems through randomization. (English) Zbl 0736.60066
Numerical solution of Markov chains, Pap. Workshop 1990, Probab., Pure Appl. 8, 357-371 (1991).
Summary: A. Jensen [Skand. Aktuarietidskr. 1953 (36), 87–91 (1953; Zbl 0051.35607)] proposed a very efficient method to find transient solutions of continuous-time Markov chains. This method, known by the names “randomization” or “uniformization”, has become very popular. We describe Jensen’s method in the setting of Markovian event systems, and we show its potentials and limitations. We also point out the importance of transient solutions in general, and we show that in many cases of interest, transient solutions are more easily obtained than equilibrium solutions.
[For the entire collection see Zbl 0733.00019.]

MSC:
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
65C99 Probabilistic methods, stochastic differential equations