Ergodic theory and a local occupation time for measure-valued critical branching brownian motion

1 September 1986

journal article
research article
Published by Taylor & Francis in Stochastics

Vol. 18 (3-4) , 197-243
https://doi.org/10.1080/17442508608833409

Abstract

Let (X_t)t>=0 denote the measure-valued critical branching Brownian motion on R^d with initial state being Lebesgue measure. A strong ergodic theorem is proved for (X_t)_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.

Keywords

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