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The characteristic of the diagonal Q-matrix with instantaneous states. (Chinese. English summary) Zbl 0704.60076

Summary: Let E denote a finite or denumerable set, a matrix \(Q=(q_{ij}\); i,j\(\in E)\) is called a Q matrix if there is a standard and homogeneous Markov chain P(t) such that \(P'(0)=Q\). Further, \(Q=P'(0)\) is called an honest Q- matrix if P(t) is honest (namely, \(\sum_{j\in E}p_{ij}(t)=1\), \(\forall i\in E)\). We give criteria for the diagonal matrix \(Q=(q_{ij}\); i,j\(\in E)\) \((q_{ij}=0\), \(i\neq j)\) to be a Q-matrix and to be an honest Q-matrix.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
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