Three different results are established which turn out to be closely
connected so that the first one implies the second one which in turn
implies the third one. The first one states the smoothness of an
invariant diffusion density
with respect to a parameter. The second establishes a similar smoothness
of the solution of the Poisson equation in $\mathbb{R}^d$.
The third one states a diffusion approximation result, or in other words
an averaging of singularly perturbed diffusion for
"fully coupled SDE systems'' or "SDE systems with complete
dependence.''
Publié le : 2003-07-14
Classification:
Diffusion approximation,
Poisson equation with parameter,
invariant density with parameter,
Green function with parameter.,
60H10,
60J17,
35J15,
35B30
@article{1055425774,
author = {Pardoux, \`E. and Veretennikov, A. Yu.},
title = {On Poisson equation and diffusion approximation 2},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 1166-1192},
language = {en},
url = {http://dml.mathdoc.fr/item/1055425774}
}
Pardoux, È.; Veretennikov, A. Yu. On Poisson equation and diffusion approximation 2. Ann. Probab., Tome 31 (2003) no. 1, pp. 1166-1192. http://gdmltest.u-ga.fr/item/1055425774/