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Law of large numbers for branching symmetric Hunt processes with measure-valued branching rates
We establish weak and strong law 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 strong law
of large numbers for branching symmetric Markov processes by Chen-Shiozawa [J.
Funct. Anal., 250, 374--399, 2007] and for branching diffusions by
Engl\"ander-Harris-Kyprianou [Ann. Inst. Henri Poincar\'e Probab. Stat., 46,
279--298, 2010]. Our results can be applied to some interesting examples that
are covered by neither of these papers
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