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.
