´ Franc Universite ¸ ois Rabelais Tours / University of Sciences of Ho Chi Minh City M2 report in mathematics 2014/2015

On the Galton-Watson processes ´ Marc PEIGNE,

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Summary. We describe the classical properties of Galton-Watson processes with non degenerated offspring distribution : extinction probability, tail of the extinction time distribution, description of supercritical, critical and subcritical cases, asymptotic growth in the supercritical case, conditioned Galton-Watson processes, multi-type Galton-Watson processes ... If it remains time, we will also describe the first properties the 3 types of behaviors of branching random walks. References. Geiger J. Elementary new proofs of classical limit theorems for Galton-Watson processes J. App. Prob. 1999, vol. 36, pp. 301-309-751 Harris T.E. The theory of branching processes , Dover Phoennix Edition, Chap 1. Lalley S. Branching Processes, http ://galton.uchicago.edu/ lalley/Courses/312/Branching.pdf Woess W. Denumerable Markov Chains, EMS Edition (2009).

´ LMPT, UMR 7350, Facult´e des Sciences et Techniques, Parc de Grandmont, 1. Marc PEIGNE, 37200 Tours. [email protected] 1

On the Galton-Watson processes

301-309-751. Harris T.E. The theory of branching processes , Dover Phoennix Edition, Chap 1. Lalley S. Branching Processes, http ://galton.uchicago.edu/ ...
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