On convergence rate estimates for some birth and death processes. (English. Russian original) Zbl 1373.82052
J. Math. Sci., New York 221, No. 4, 616-622 (2017); translation from Statisticheskie Metody Otsenivaniya i Proverki Gipotez 20, 140-148 (2007).
Summary: Homogeneous birth and death processes with a finite number of states are studied. We analyze the slowest and fastest rates of convergence to the limit mode. Estimates of these bounds for some classes of mean-field models are obtained. The asymptotics of the convergence rate for some models of chemical kinetics is studied in the case where the number of system states tends to infinity.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 37A60 | Dynamical aspects of statistical mechanics |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
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