The Annals of Probability

On the Filtration of Historical Brownian Motion

Martin T. Barlow and Edwin A. Perkins

Full-text: Open access

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 $\beta \in (0, 1\rbrack$.

Article information

Source
Ann. Probab., Volume 22, Number 3 (1994), 1273-1294.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988603

Digital Object Identifier
doi:10.1214/aop/1176988603

Mathematical Reviews number (MathSciNet)
MR1303645

Zentralblatt MATH identifier
0816.60044

JSTOR
links.jstor.org

Subjects
Primary: 60G57: Random measures
Secondary: 60G07: General theory of processes

Keywords
Superprocesses historical processes branching measure-valued diffusions

Citation

Barlow, Martin T.; Perkins, Edwin A. On the Filtration of Historical Brownian Motion. Ann. Probab. 22 (1994), no. 3, 1273--1294. doi:10.1214/aop/1176988603. https://projecteuclid.org/euclid.aop/1176988603


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