Supercritical Markov branching processes with general set of types

Asymptotic behaviour of immigration-branching processes by general set of types. II: Supercritical branching part

We construct an immigration-branching process from an inhomogeneous Poisson process, a parameter-dependent probability distribution of populations and a Markov branching process with homogeneous transition function. The set of types is arbitrary, and the parameter is allowed to be discrete or continuous. Assuming a supercritical branching part with primitive first moments and finite second moments, we prove propositions on the mean square convergence and the almost sure convergence of normalized averaging processes associated with the immigration-branching process.

Asymptotic behaviour of immigration-branching processes by general set of types. II: Supercritical branching part

We construct an immigration-branching process from an inhomogeneous Poisson process, a parameter-dependent probability distribution of populations and a Markov branching process with homogeneous transition function. The set of types is arbitrary, and the parameter is allowed to be discrete or continuous. Assuming a supercritical branching part with primitive first moments and finite second moments, we prove propositions on the mean square convergence and the almost sure convergence of normalized averaging processes associated with the immigration-branching process.

Coupling and the Non-degeneracy of the Limit in Some Plasmid Reproduction Models

We settle a problem raised by Seneta and Tavare concerning the normalized limits of several plasmid reproduction models. We also show that for countably infinitely many type branching processes the extinction probability and the mass at the origin of the supercritical limit need not be the same, in contrast to the finite type case. Copyright 1997 Academic Press