Abstract
We show that the historical Brownian motion may be recovered from ordinary super-Brownian motion when the dimension $d$ of the underlying Brownian motion is greater than 4. We outline a proof showing that this conclusion is false if $d \leq 3$. The state of affairs in the critical dimension $d = 4$ is left unresolved. Some extensions are given for $1 + \beta$ stable branching mechanisms where $\beta \in (0, 1\rbrack$.
Citation
Martin T. Barlow. Edwin A. Perkins. "On the Filtration of Historical Brownian Motion." Ann. Probab. 22 (3) 1273 - 1294, July, 1994. https://doi.org/10.1214/aop/1176988603
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