Asymptotics of continuous-time discrete state space branching processes for large initial state

Martin Möhle; Benedict Vetter

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arXiv · 2002.05940

Asymptotics of continuous-time discrete state space branching processes for large initial state

Martin Möhle·Benedict Vetter

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Abstract

Scaling limits for continuous-time branching processes with discrete state space are provided as the initial state tends to infinity. Depending on the finiteness or non-finiteness of the mean and/or the variance of the offspring distribution, the limits are in general time-inhomogeneous Gaussian processes, time-inhomogeneous generalized Ornstein-Uhlenbeck type processes or continuous-state branching processes. We also provide transfer results showing how specific asymptotic relations for the probability generating function of the offspring distribution carry over to those of the one-dimensional distributions of the branching process.

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Martin Möhle, Benedict Vetter. 2020-02-14. Asymptotics of continuous-time discrete state space branching processes for large initial state. https://arxiv.org/abs/2002.05940

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