Statistics Seminars: Measure change in multitype branching: bushes to trees
16 November 2001 14:00 in CM221
"A classical result for the Galton-Watson process, in which each person gives rise to an independent number of children according to a single family size distribution, is that the martingale formed by normalizing the size of the nth generation by its expectation converges in mean exactly when the family size distribution has a finite XlogX moment. Any martingale induces (or is) a change of measure. By identifying and using the new measure, Lyons, Pemantle and Peres, provided a new proof of the classical result in 1995. Viewed in the right way, the change of measure turns the branching bush that is the Galton-Watson process (in which every family looks the same) into a tree with a trunk, where branching from the trunk is different from elsewhere. The classical martingale arises naturally from a (very simple!) function that is 'harmonic in mean'. The aim of this talk will be to show how the proof works and, with this concept of 'harmonic in mean', extends. "
"Department of Probability and Statistics, University of Sheffield"
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