On the Poisson equation and diffusion approximation 3

Pardoux, E.; Veretennikov, A. Yu.

Ann. Probab., Tome 33 (2005) no. 1, p. 1111-1133 / Harvested from Project Euclid

Résumé

We study the Poisson equation Lu+f=0 in ℝ^d, where L is the infinitesimal generator of a diffusion process. In this paper, we allow the second-order part of the generator L to be degenerate, provided a local condition of Doeblin type is satisfied, so that, if we also assume a condition on the drift which implies recurrence, the diffusion process is ergodic. The equation is understood in a weak sense. Our results are then applied to diffusion approximation.

Publié le : 2005-05-14
Classification: Poisson equation, degenerate diffusion, diffusion approximation, 60F17, 60J60, 35J70

@article{1115386720,
     author = {Pardoux, E. and Veretennikov, A. Yu.},
     title = {On the Poisson equation and diffusion approximation 3},
     journal = {Ann. Probab.},
     volume = {33},
     number = {1},
     year = {2005},
     pages = { 1111-1133},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1115386720}
}

Pardoux, E.; Veretennikov, A. Yu. On the Poisson equation and diffusion approximation 3. Ann. Probab., Tome 33 (2005) no. 1, pp.  1111-1133. http://gdmltest.u-ga.fr/item/1115386720/