A pathwise iterative approach to the extinction of branching processes\n with countably many types

2016/05/10 by Peter Braunsteins, Braunsteins, Peter, Geoffrey Decrouez +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1605.03069

openalex publication_date 2016/05/10 · openalex created_date 2022/09/15 · openalex updated_date 2026/07/28

Abstract

We consider the extinction events of Galton-Watson processes with countably\ninfinitely many types. In particular, we construct truncated and augmented\nGalton-Watson processes with finite but increasing sets of types. A pathwise\napproach is then used to show that, under some sufficient conditions, the\ncorresponding sequence of extinction probability vectors converges to the\nglobal extinction probability vector of the Galton-Watson processes with\ncountably infinitely many types. This gives rise to a number of iterative\nmethods for the computation of the global extinction probability vector.\n

Citations

• General linear-fractional branching processes with discrete time

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