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Let $G$ be a Galton-Watson tree, i.e. the family tree of a Galton-Watson branching process. For $0 \leq u \leq 1$ let $G_u$ be the subtree of $G$ obtained by retaining each edge with probability $u$ and deleting other edges. We study the tree-valued Markov process $(G_u, 0 \leq u \leq 1)$ and an analogous process $(G^*_u, 0 \leq u \leq 1)$ in which $G^*_1$ is a critical or subcritical Galton-Watson tree conditioned to be infinite. Results simplify and are further developed in the special case of Poisson$(\mu)$ offspring distribution.

Details

Title
Tree-valued Markov chains derived from Galton-Watson processes.
Creator
Aldous, David, Author
Pitman, Jim, Author
Published
Statistics Department, University of California, Berkeley, University of California at Berkeley, Berkeley, California, Feb 1997
Full Collection Name
Statistics Technical Reports
Other Identifiers
481
Type
Text
Format
technical reports
Archive
Mathematics Statistics Library
Note
Ann. Inst. Henri. Poincar\'e 34, 1998, 637-686
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