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Some remarks on the duality of continuous time Markov chains. (English) Zbl 0721.60081
Summary: A simple proof of D. Siegmund’s result [Ann. Probab. 4, 914-924 (1976; Zbl 0364.60109)] on the relation between dual q-matrices and dual transition functions for Markov chains is given. A byproduct is a uniqueness result for minimal solutions of stochastically monotone q- matrices.

MSC:
60J27 Continuous-time Markov processes on discrete state spaces
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References:
[1] Chung K.L., Markov chains with stationary transition probabilities (1967) · Zbl 0146.38401
[2] DOI: 10.1214/aop/1176993008 · Zbl 0563.60062
[3] DOI: 10.1090/S0002-9947-1957-0094854-8
[4] DOI: 10.1007/BF02392391 · Zbl 0079.34703
[5] DOI: 10.1112/jlms/s2-5.2.267 · Zbl 0246.60064
[6] DOI: 10.1214/aop/1176995936 · Zbl 0364.60109
[7] Van Doom E.A., Stochastic Monotonicity and Queueing Applications of Birth-death Processes 4 (1980)
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