Entropy and convergence in dynamics and demography
The paper starts with a review of some results by \textit{S. Goldstein} and \textit{O. Penrose} [J. Stat. Phys. 24, 325-342 (1981; Zbl 0516.70021)] on the relation between convergence rate, Kullback information, and Kolmogorov-Sinai entropy for irreducible, aperiodic finite Markov chains (including the effects of time-scaling and of coarse-graining of the state space). Elementary proofs of such results are provided. The transformation of the standard demographic Leslie projection model into a Markov chain is reviewed. An expression for the entropy in terms of the eigenvalues of the Leslie matrix is obtained. When there is a stable age distribution, the demographic meaning of the entropy is discussed in connection with the convergence rate. Finally, imprimitive and periodic limits and the relation to population entropy are discussed.
irreducible, aperiodic finite Markov chains
scientific article; zbMATH DE number 219779
scientific article