Decay parameter and related properties of n-type branching processes

作者：Li JunPing^*; Wang Juan

来源：Science China Mathematics, 2012, 55(12): 2535-2556.

DOI：10.1007/s11425-012-4466-z

• n-type Markov branching process
• decay parameter
• invariant measures
• invariant vectors
• quasi-stationary distributions

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 lambda(C) of such model is given for the communicating class C = Z(+)(n)\0. It is shown that this lambda(C) can be directly obtained from the generating functions of the corresponding q-matrix. Moreover, the

• 出版日期2012-12
• 单位中南大学