First-passage times and related moments for continuous-time birth-death chains. (English) Zbl 1427.60163
Summary: First-passage time problems for continuous-time birth-death chains are considered. Recursive formulas for the moments of the first-exit time and of the first-passage time in terms of the potential coefficients are explicitly obtained. Making use of the probability current, some functional relations between transition probabilities for unrestricted and restricted continuous-time birth-death chains are determined. Finally, two continuous-time birth-death chains with constant rates are taken in account; for them, closed form results on the first-exit time and on the first-passage time are explicitly obtained.
MSC:
| 60J27 | Continuous-time Markov processes on discrete state spaces |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
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