Volume 20, 2016
|Page(s)||400 - 416|
|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
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.