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Ergodic theory and a local occupation time for measure-valued critical branching Brownian motion. (English) Zbl 0608.60077
Author’s abstract: Let $$(X_ t)_{t\geq 0}$$ denote the measure-valued critical branching Brownian motion on $${\mathbb{R}}^ d$$ with initial state being Lebesgue measure. A strong ergodic theorem is proved for $$(X_ t)_{t\geq 0}$$ when $$d\geq 3$$, 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.
Reviewer: D.Dawson

##### MSC:
 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60J60 Diffusion processes
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