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Mathematical Sciences

Galton-Watson branching processes and related discrete distributions

Date: 3:30pm PST November 10, 2016 Location: John Howard 132

John Howard 132

Galton-Watson branching processes and related discrete distributions

 by Assistant Professor Violetta E. Piperigou
Department of Mathematics, University of Patras, Greece

The Galton-Watson branching process is the oldest, simplest and best known branching process. Its simplicity makes it an appropriate and frequently employed tool for the introductory study of the processes of proliferation in biology and the description of extinction phenomena.

When the probability generating function (p.g.f.) of the descendants is of a fractional linear form, the p.g.f. of the distribution of the individuals in the nth generation can be written as a ratio of p.g.f.’s of two geometric distributions. The general problem of determining the conditions that allow a ratio of two p.g.f.’s to be the p.g.f. of a discrete non-negative random variable is here considered and various such examples are presented.

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