Janos Englander

University of California at Santa Barbara



Title: "Strong Law of Large Numbers for Branching Diffusions"


Establishing a Law of Large Numbers for spatial branching diffusions has been investigated by several people starting with Watanabe in the sixties, Asmussen and Hering in the seventies  and it is continued very recently  by Chen et al. (2008). Similar questions have recently been studied forsuperprocesses by Turaev, Winter and the speaker and by Chen  et al. In the talk I will report on new work where under very general conditions, the Strong Law has been proven. Unlike earlier work, the new method is more probabilistic than analytic as it is based on a "spine" (sometimes called "backbone") decomposition for branching diffusions. Although spine-decompositions are well known in the literature since the pioneering work of Lyons, Pemantle and Peres,  this  seems to be the  first time when it is applied  for the SLLN.  This is joint work with Simon Harris and Andreas Kyprianou (Bath, UK).