We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the classical continuous-state branching processes and Markov branching processes. Several results such as the expressions of moments and the branching inequality governing the evolution of the process are presented and commented. The generalized Feller branching diffusion and the fractional Yule process are analyzed in detail as special cases of the general model.

On a class of Time-fractional Continuous-state Branching Processes

ANDREIS, LUISA;Federico Polito;Laura Sacerdote
2017

Abstract

We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the classical continuous-state branching processes and Markov branching processes. Several results such as the expressions of moments and the branching inequality governing the evolution of the process are presented and commented. The generalized Feller branching diffusion and the fractional Yule process are analyzed in detail as special cases of the general model.
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https://arxiv.org/pdf/1702.03188
Continuous-state Branching Processes, Time-change, Subordinators
Andreis, Luisa; Polito, Federico; Sacerdote, Laura Lea
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1652402
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