Open Access
July, 1994 On the Filtration of Historical Brownian Motion
Martin T. Barlow, Edwin A. Perkins
Ann. Probab. 22(3): 1273-1294 (July, 1994). DOI: 10.1214/aop/1176988603
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 $\beta \in (0, 1\rbrack$.

Copyright © 1994 Institute of Mathematical Statistics
Martin T. Barlow and Edwin A. Perkins "On the Filtration of Historical Brownian Motion," The Annals of Probability 22(3), 1273-1294, (July, 1994). https://doi.org/10.1214/aop/1176988603
Published: July, 1994
Vol.22 • No. 3 • July, 1994
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