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Resolvent decomposition theorems and Kolmogorov \(Q\)-process. (Chinese. English summary) Zbl 1488.60187

Summary: The main aim of this paper is to use the resolvent decomposition theorems to analyzing the Kolmogorov \(Q\)-process which has finitely many instantaneous states. After obtaining an elegant condition for existence and uniqueness, we focus on discussing all kinds of properties of such subtle process. In particular, we show that the Kolmogorov \(Q\)-process is always recurrent and then an easy-checking condition for positive recurrence is obtained. The closed form for the limiting distribution is explicitly expressed. The symmetry and reversibility of such process are also discussed and well-answered.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
60J35 Transition functions, generators and resolvents
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