On the Poisson Equation and Diffusion Approximation. I
Pardoux, E. ; Veretennikov, Yu.
Ann. Probab., Tome 29 (2001) no. 1, p. 1061-1085 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
A Poisson equation in $\mathbb{R}^d$ for the elliptic operator corresponding to an ergodic diffusion process is considered. Existence and uniqueness of its solution in Sobolev classes of functions is established along with the bounds for its growth. This result is used to study a diffusion approximation for two-scaled diffusion processes usingthe method of corrector; the solution of a Poisson equation serves as a corrector.
Publié le : 2001-07-14
Classification:  Poisson equation,  polynomial recurrence,  diffusion approximation,  60H30,  60J45,  60J60,  35J15 
@article{1015345596,
     author = {Pardoux, E. and Veretennikov, Yu.},
     title = {On the Poisson Equation and Diffusion Approximation. I},
     journal = {Ann. Probab.},
     volume = {29},
     number = {1},
     year = {2001},
     pages = { 1061-1085},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1015345596}
}

Pardoux, E.; Veretennikov, Yu. On the Poisson Equation and Diffusion Approximation. I. Ann. Probab., Tome 29 (2001) no. 1, pp.  1061-1085. http://gdmltest.u-ga.fr/item/1015345596/