An effective criterion and a new example for ballistic diffusions in random environment
| dc.creator | Goergen, Laurent | |
| dc.date | 2007-06-27 | |
| dc.date | 2008-06-16 | |
| dc.date.accessioned | 2026-07-07T09:44:22Z | |
| dc.date.available | 2026-07-07T09:44:22Z | |
| dc.description | In the setting of multidimensional diffusions in random environment, we carry on the investigation of condition $(T')$, introduced by Sznitman [Ann. Probab. 29 (2001) 723--764] and by Schmitz [Ann. Inst. H. Poincaré Probab. Statist. 42 (2006) 683--714] respectively in the discrete and continuous setting, and which implies a law of large numbers with nonvanishing limiting velocity (ballistic behavior) as well as a central limit theorem. Specifically, we show that when $d\geq2$, $(T')$ is equivalent to an effective condition that can be checked by local inspection of the environment. When $d=1$, we prove that condition $(T')$ is merely equivalent to almost sure transience. As an application of the effective criterion, we show that when $d\geq4$ a perturbation of Brownian motion by a random drift of size at most $ε>0$ whose projection on some direction has expectation bigger than $ε^{2-η},η>0$, satisfies condition $(T')$ when $ε$ is small and hence exhibits ballistic behavior. This class of diffusions contains new examples of ballistic behavior which in particular do not fulfill the condition in [Ann. Inst. H. Poincaré Probab. Statist. 42 (2006) 683--714], (5.4) therein, related to Kalikow's condition. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AOP354 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0706.4069 | |
| dc.identifier | http://arxiv.org/abs/0706.4069 | |
| dc.identifier | Annals of Probability 2008, Vol. 36, No. 3, 1093-1133 | |
| dc.identifier | doi:10.1214/07-AOP354 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162851 | |
| dc.subject | Probability | |
| dc.subject | 60K37, 82D30 (Primary) | |
| dc.title | An effective criterion and a new example for ballistic diffusions in random environment | |
| dc.type | text |