We study the behavior for large $|x|$ of Kunita-type stochastic
flows $\phi(t, \omega x)$ on $R^d$, driven by continuous spatial
semimartingales. For this class of flows we prove new spatial estimates for
large $|x|$, under very mild regularity conditions on the driving
semimartingale random field. It is expected that the results would be of
interest for the theory of stochastic flows on noncompact manifolds as well as
in the study of nonlinear filtering, stochastic functional and partial
differential equations. Some examples and counterexamples are given.
Publié le : 1998-01-14
Classification:
Stochastic flow,
spacial semimartingale,
local characteristics,
quadratic variation,
stochastic differential equation (s.d.e.),
60H10,
60H20,
60H25
@article{1022855411,
author = {Mohammed, Salah-Eldin A. and Scheutzow, Michael K. R.},
title = {Spatial estimates for stochastic flows in Euclidean
space},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 56-77},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855411}
}
Mohammed, Salah-Eldin A.; Scheutzow, Michael K. R. Spatial estimates for stochastic flows in Euclidean
space. Ann. Probab., Tome 26 (1998) no. 1, pp. 56-77. http://gdmltest.u-ga.fr/item/1022855411/