Abstract
Let (Xt)t>=0 denote the measure-valued critical branching Brownian motion on Rd with initial state being Lebesgue measure. A strong ergodic theorem is proved for (Xt)t>=0 when d>=3, while a weak ergodic theorem is proved for d = 2. Also a weak local occupation time (an analogue of the local time for Brownian motion) is shown to exist in dimensions d=1,2 and 3.
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