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Branching Processes in Autoregressive Random Environment

By Penka Mayster


2000 Mathematics Subject Classification: 60J80, 60K05.We consider the model of alternating branching processes where two Markov branching processes act alternately at random observation and treatment times. The sequences of cycles (observation, treatment) = (δn, τn) constitute a random environment for branching mechanisms. We suppose in addition that the lengths of the cycles σ n = δn + τn are generated by the linear additive first order autoregressive schema EAR(1)

Topics: controlled branching process, state-dependent emigration, random environment, extinction probability, limit theorem in the supercritical case
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Year: 2009
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