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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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