controlled branching process state-dependent emigration random environment extinction probability limit theorem in the supercritical case
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 19, No 1, (2009), 217p-228p
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).