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On the Poisson equation and diffusion approximation 3 | | E. Pardoux
; A. Yu. Veretennikov
; | | Date: |
29 Jun 2005 | | Journal: | Annals of Probability 2005, Vol. 33, No. 3, 1111-1133 DOI: 10.1214/009117905000000062 | | Subject: | Probability MSC-class: 60F17, 60J60, 35J70 (Primary) | math.PR | | Abstract: | 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. | | Source: | arXiv, math.PR/0506596 | | Services: | Forum | Review | PDF | Favorites | |
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