| Issue |
ESAIM: PS
Volume 20, 2016
|
|
|---|---|---|
| Page(s) | 400 - 416 | |
| DOI | https://doi.org/10.1051/ps/2016019 | |
| Published online | 30 November 2016 | |
Conditioned multi-type Galton−Watson trees
Institute for Mathematics, Astrophysics, and Particle Physics, Faculty of
Science, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, the
Netherlands.
e.cator@math.ru.nl, henkdon@gmail.com
Received:
22
July
2015
Revised:
19
February
2016
Accepted:
13
July
2016
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.
Mathematics Subject Classification: 60J80
Key words: Multi-type Galton−Watson tree / conditioning / recursive events
© EDP Sciences, SMAI 2016
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