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Defective Galton-Watson processes

Serik Sagitov (Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik) ; C. Minuesa
Stochastic Models (1532-6349). Vol. 33 (2017), 3, p. 451-472.
[Artikel, refereegranskad vetenskaplig]

The Galton-Watson process is a Markov chain modeling the population size of independently reproducing particles giving birth to k offspring with probability p(k), k 0. In this paper, we consider defective Galton-Watson processes having defective reproduction laws, so that Sigma(k 0)p(k) = 1 - E for some E (0, 1). In this setting, each particle may send the process to a graveyard state with probability E. Such a Markov chain, having an enhanced state space {0, 1, ...}{}, gets eventually absorbed either at 0 or at . Assuming that the process has avoided absorption until the observation time t, we are interested in its trajectories as t and E 0.

Nyckelord: Branching process, conditional limit theorems, defective distribution, Galton-Watson process with killing

Denna post skapades 2018-01-10.
CPL Pubid: 254409


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Institutionen för matematiska vetenskaper, Tillämpad matematik och statistikInstitutionen för matematiska vetenskaper, Tillämpad matematik och statistik (GU)



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