Abstract

The Kesten-Stigum theorem for the one-type Galton-Watson process gives necessary
and sufficient conditions for mean convergence of the martingale formed
by the population size normed by its expectation. Here, the approach of Lyons,
Peres and Pemantle (1995) to this theorem, which exploits a change of measure
argument, is extended to martingales defined on Galton-Watson
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