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Zbl 0587.92017
Cohen, Joel E.
Multiregional age-structured populations with changing rates: Weak and stochastic ergodic theorems. (English)
[A] Multidimensional mathematical demography, Proc. Conf. Univ. Md., College Park/Md. 1981, 477-503 (1982).

[For the entire collection see Zbl 0564.00025.] \par The purposes of this chapter are to describe some population models in which serial and parallel inhomogeneity are combined, and to state some ergodic theorems for these models. \par In demography, ergodic theorems describe long-run behavior that is independent of initial conditions. Weak ergodic theorems assume that the rates that govern a population's evolution themselves follow some deterministic trajectory. {\it H. Le Bras} [Une formulation générale de la dynamique des populations. Population, Spec. Vol.: "La mesure des phénomènes demographiques", 261-290 (1977)] gave the first weak ergodic theorem for multiregional age-structured populations. \par We shall give four weak ergodic theorems that are more general than that of Le Bras. Stochastic ergodic theorems assume that the rates that govern a population's evolution are selected from a set of possible rates by some stochastic process. We shall state a stochastic ergodic theorem that assumes that the rates of birth, death, and migration or other transition are selected by a Markov chain.

MSC 2000:: *92D25 Population dynamics
60J10 Markov chains with discrete parameter
15A99 Miscellaneous topics in linear algebra

Keywords: multistate projection matrices; population models; serial and parallel inhomogeneity; demography; multiregional age-structured populations; weak ergodic theorems; stochastic ergodic theorem; birth; death; migration; transition

Citations: Zbl 0564.00025

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