Inhomogeneous Markov branching processes: Supercritical case

H. Cohn and H. Hering

Stochastic Processes and their Applications, 1983, vol. 14, issue 1, 79-91

Abstract: It is our aim to improve the limit theory of supercritical Bienaymé--Galton--Watson processes with varying environment (cf. [3], [4]), and to simultaneously construct its continuous-time analogue. We give a necessary and sufficient condition for the existence of a non-degenerate limit with expectation norming and show that if the limit is non-degenerate, its expectation must be equal to 1. We continue with a result on the expectation of the limit in case of general norming and conditions for the continuity and strict monotonicity of the limiting distribution function. Finally, we reformulate the non-degeneracy condition.

Keywords: Inhomogeneous; Markov; processes; varying; environment; differential; equation; branching; supercritical; limit; theorem (search for similar items in EconPapers)
Date: 1983
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Citations: View citations in EconPapers (9)

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