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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
DOI: 10.2307/3213024
Stable URL: http://www.jstor.org/stable/3213024
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Moments for a General Branching Process in a Semi-Markovian Environment
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Abstract

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.

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