On the Filtration of Historical Brownian Motion
Barlow, Martin T. ; Perkins, Edwin A.
Ann. Probab., Tome 22 (1994) no. 4, p. 1273-1294 / Harvested from Project Euclid
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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 $\beta \in (0, 1\rbrack$.
Publié le : 1994-07-14
Classification:  Superprocesses,  historical processes,  branching measure-valued diffusions,  60G57,  60G07 
@article{1176988603,
     author = {Barlow, Martin T. and Perkins, Edwin A.},
     title = {On the Filtration of Historical Brownian Motion},
     journal = {Ann. Probab.},
     volume = {22},
     number = {4},
     year = {1994},
     pages = { 1273-1294},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988603}
}

Barlow, Martin T.; Perkins, Edwin A. On the Filtration of Historical Brownian Motion. Ann. Probab., Tome 22 (1994) no. 4, pp.  1273-1294. http://gdmltest.u-ga.fr/item/1176988603/