Conditioned multi-type Galton−Watson trees
Cator, Eric1 ; Don, Henk1
1 Institute for Mathematics, Astrophysics, and Particle Physics, Faculty of Science, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, the Netherlands.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 400-416.

We consider multi-type Galton Watson trees, and find the distribution of these trees when conditioning on very general types of recursive events. It turns out that the conditioned tree is again a multi-type Galton Watson tree, possibly with more types and with offspring distributions depending on the type of the father node and on the height of the father node. These distributions are given explicitly. We give some interesting examples for the kind of conditioning we can handle, showing that our methods have a wide range of applications.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016019
Classification : 60J80
Mots clés : Multi-type Galton−Watson tree, conditioning, recursive events
Cator, Eric 1 ; Don, Henk 1

1 Institute for Mathematics, Astrophysics, and Particle Physics, Faculty of Science, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, the Netherlands. 
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     title = {Conditioned multi-type {Galton\ensuremath{-}Watson} trees},
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Cator, Eric; Don, Henk. Conditioned multi-type Galton−Watson trees. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 400-416. doi : 10.1051/ps/2016019. http://www.numdam.org/articles/10.1051/ps/2016019/

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