Ergodicity of Age Structure in Populations with Markovian Vital Rates, 111: Finite-state Moments and Growth Rate; an Illustration
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چکیده
Leslie (1945) models the evolution in discrete time of a closed, single-sex population with discrete age groups by multiplying a vector describing the age structure by a matrix containing the birth and death rates. We suppose that successive matrices are chosen according to a Markov chain from a finite set of matrices. We find exactly the long-run rate of growth and expected age structure. We give two approximations to the variance in age structure and total population size. A numerical example illustrates the ergodic features of the model using Monte Carlo simulation, finds the invariant distribution of age structure from a linear integral equation, and calculates the moments derived here. ERGODIC SETS; LESLIE MATRICES; NON-NEGATIVE MATRICES; POPULATION DYNAMICS; PRODUCTS OF RANDOM MATRICES; STOCHASTIC POPULATION MODELS
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