The demographic variation process of branching random fields. (English) Zbl 0657.60051
Author’s summary: A branching random field with immigration is considered. The demographic variation process is a non-Markovian signed measure-valued process which measures the changes in the system due to branchings and deaths in the population. The asymptotic behavior of this process under various scalings is studied. It is shown that the fluctuation limits are generalized Gaussian processes which are Markovian if and only if the branching is critical, in which case they are non- stationary generalized Ornstein-Uhlenbeck processes.
Reviewer: D.A.Dawson
MSC:
| 60F17 | Functional limit theorems; invariance principles |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60G20 | Generalized stochastic processes |
Keywords:
generalized Langevin equation; functional central limit theorem; branching random field with immigration; measure-valued process; generalized Gaussian processes; generalized Ornstein-Uhlenbeck processesReferences:
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