On a bilateral birth-death process with alternating rates. (English) Zbl 1301.60099
Summary: We consider a bilateral birth-death process characterized by a constant transition rate \(\lambda\) from even states and a possibly different transition rate \(\mu\) from odd states. We determine the probability generating functions of the even and odd states, the transition probabilities, mean and variance of the process for arbitrary initial states. Some features of the birth-death process confined to the non-negative integers by a reflecting boundary in the zero-state are also analyzed. In particular, making use of a Laplace transform approach, we obtain a series form of the transition probability from state 1 to the zero-state.
MSC:
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60J85 | Applications of branching processes |
Keywords:
birth-death processes; alternating rates; probability generating functions; transition probabilities; symmetryReferences:
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