The superprocess and its occupation time process are represented as
Hilbert space valued solutions of stochastic evolution equations by using the
Fourier transform of the process. For appropriate parameter values, the
existence of density valued solutions follows. Pathwise regularity of the
processes is obtained.As a new tool we develop a maximal inequality. We also
extend the Tanaka-like evolution equations developed for local time processes
and provide an Ito formula for certain functionals of the superprocess.
Publié le : 2000-01-14
Classification:
Superprocess,
Sobolev space regularity,
stochastic evolution equation,
occupation times,
60617,
60G20,
60G57,
60H15
@article{1019160113,
author = {Blount, D. and Bose, A.},
title = {Hilbert space regularity of the $(\alpha,d,1)$-superprocess and
its occupation time},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 104-131},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160113}
}
Blount, D.; Bose, A. Hilbert space regularity of the $(\alpha,d,1)$-superprocess and
its occupation time. Ann. Probab., Tome 28 (2000) no. 1, pp. 104-131. http://gdmltest.u-ga.fr/item/1019160113/