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A branching-selection process related to censored Galton–Walton processes

Olivier Couronné, Lucas Gerin (2014)

Annales de l'I.H.P. Probabilités et statistiques

We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré [Comm. Math. Phys.298 (2010) 323–342]. The proof is based on a connection with a supercritical Galton–Watson process censored at a certain level.

A nonasymptotic theorem for unnormalized Feynman–Kac particle models

F. Cérou, P. Del Moral, A. Guyader (2011)

Annales de l'I.H.P. Probabilités et statistiques

We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first...

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

González, M., Martínez, R., Mota, M. (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 60J80.In this work, the problem of the limiting behaviour of an irreducible Multitype Galton-Watson Branching Process with period d greater than 1 is considered. More specifically, almost sure convergence of some linear functionals depending on d consecutive generations is studied under hypothesis of non extinction. As consequence the main parameters of the model are given a convenient interpretation from a practical point of view. For a better understanding...

A stochastic fixed point equation for weighted minima and maxima

Gerold Alsmeyer, Uwe Rösler (2008)

Annales de l'I.H.P. Probabilités et statistiques

Given any finite or countable collection of real numbers Tj, j∈J, we find all solutions Fto the stochastic fixed point equation W = d inf j J T j W j , whereW and the Wj, j∈J, are independent real-valued random variables with distribution Fand = d means equality in distribution. The bulk of the necessary analysis is spent on the case when |J|≥2 and all Tj are (strictly) positive. Nontrivial solutions are then concentrated on either the positive or negative half line. In the most interesting (and difficult) situation T...

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