On the problem of optimal instant observations of the linear birth and death process. (English) Zbl 1333.60187
Summary: The problem of the optimal intensity of instant observations of the processes of birth and death with linear growth and immigration is considered. Results are obtained for the objective function calculated as an expected normalized linear function of the number of observations and an expected normalized quadratic form of the errors of estimation, given instant observations.
MSC:
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60G50 | Sums of independent random variables; random walks |
| 62M05 | Markov processes: estimation; hidden Markov models |
| 93E20 | Optimal stochastic control |
Keywords:
birth-and-death process; random walk; instant observations; intensity; optimization; martingaleReferences:
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