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Moments for a General Branching Process in a Semi-Markovian Environment
Craig Whittaker and Richard M. Feldman
Journal of Applied Probability
Vol. 17, No. 2 (Jun., 1980), pp. 341-349
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3213024
Page Count: 9
You can always find the topics here!Topics: Mathematical moments, Population size, Random variables, Population mean, Markov processes, Population estimates, Insect pests, Temperature dependence, Children, Mathematical theorems
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A general branching process is extended to allow life length and reproduction probabilities to depend on randomly changing environmental states. First and second moments of the population size with respect to time are derived assuming that the environmental process is semi-Markovian. The results are similar to Markov-renewal type equations which allow, under discrete time, iterative computation of both moments of the population through time.
Journal of Applied Probability © 1980 Applied Probability Trust