par Louchard, Guy 
;Drmota, Michael;Yanev, N.
Référence Stochastic analysis and applications, 24, 1, page (37-59)
Publication Publié, 2006
;Drmota, Michael;Yanev, N.Référence Stochastic analysis and applications, 24, 1, page (37-59)
Publication Publié, 2006
Article révisé par les pairs
| Résumé : | Some classes of controlled branching processes (with nonhomogeneous migration or with nonhomogeneous state-dependent immigration) lead in the critical case to a recurrence for the extinction probabilities. Under some additional conditions it is known that this recurrence depends on some parameter β and converges for 0 < β < 1. Now we show that the recurrence does converge for all positive values of the parameter β, which leads to an extension of some limit theorems for the corresponding branching processes. We also give a generalization of the recurrence and an asymptotic analysis of its behavior. |
