Limits Of One Dimensional Diffusions
| dc.creator | Lowther, George | |
| dc.date | 2007-12-14 | |
| dc.date | 2008-08-17 | |
| dc.date.accessioned | 2026-07-07T13:14:15Z | |
| dc.date.available | 2026-07-07T13:14:15Z | |
| dc.description | In this paper we look at the properties of limits of a sequence of real valued time inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However, we show that as long as the drift terms satisfy a Lipschitz condition and the limit is continuous in probability, then it will lie in a class of processes that we refer to as almost-continuous diffusions. These processes are strong Markov and satisfy an `almost-continuity' condition. We also give a simple condition for the limit to be a continuous diffusion. These results contrast with the multidimensional case where, as we show with an example, a sequence of two dimensional martingale diffusions can converge to a process that is both discontinuous and non-Markov. | |
| dc.description | 32 pages. Updated to most recent version submitted to Annals of Probability | |
| dc.identifier | https://arxiv.org/abs/0712.2428 | |
| dc.identifier | http://arxiv.org/abs/0712.2428 | |
| dc.identifier | Ann. Probab. Volume 37, Number 1 (2009), 78-106 | |
| dc.identifier | doi:10.1214/08-AOP397 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230148 | |
| dc.subject | Probability | |
| dc.subject | 60J60; 60J25; 60G44; 60F99 | |
| dc.title | Limits Of One Dimensional Diffusions | |
| dc.type | text |