Abstract
We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions for n-type Markov branching processes on the basis of the 1-type Markov branching processes and 2-type Markov branching processes. Investigating such behavior is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for n-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λ C of such model is given for the communicating class C = ℤ n+ \ 0. It is shown that this λ C can be directly obtained from the generating functions of the corresponding q-matrix. Moreover, the λ C -invariant measures/vectors and quasidistributions of such processes are deeply considered. λ C -invariant measures and quasi-stationary distributions for the process on C are presented.
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Li, J., Wang, J. Decay parameter and related properties of n-type branching processes. Sci. China Math. 55, 2535–2556 (2012). https://doi.org/10.1007/s11425-012-4466-z
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DOI: https://doi.org/10.1007/s11425-012-4466-z
Keywords
- n-type Markov branching process
- decay parameter
- invariant measures
- invariant vectors
- quasistationary distributions