Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates

We establish weak and strong laws of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the branching mechanism being general and state dependent. Our work is motivated by recent work on the strong law of large numbers for branching symmetric Markov processes by Chen and Shiozawa (J Funct Anal 250:374-399, 2007) and for branching diffusions by Englander et al. (Ann Inst Henri Poincar, Probab Stat 46:279-298, 2010). Our results can be applied to some interesting examples that are covered by neither of these papers.NSF [DMS-1206276, NNSFC 11128101]; NNSFC [11271030, 11128101]; NNSF of China [11501029]; Beijing Institute of TechnologySCI(E)ARTICLE3898-9313