Rates of convergence of a transient diffusion in a spectrally negative Lévy potential
| dc.creator | Singh, Arvind | |
| dc.date | 2006-06-19 | |
| dc.date | 2008-01-02 | |
| dc.date.accessioned | 2026-07-07T08:52:13Z | |
| dc.date.available | 2026-07-07T08:52:13Z | |
| dc.description | We consider a diffusion process $X$ in a random Lévy potential $\mathbb{V}$ which is a solution of the informal stochastic differential equation \begin{eqnarray*}\cases{dX_t=dβ_t-{1/2}\mathbb{V}'(X_t) dt,\cr X_0=0,}\end{eqnarray*} ($β$ B. M. independent of $\mathbb{V}$). We study the rate of convergence when the diffusion is transient under the assumption that the Lévy process $\mathbb{V}$ does not possess positive jumps. We generalize the previous results of Hu--Shi--Yor for drifted Brownian potentials. In particular, we prove a conjecture of Carmona: provided that there exists $0<κ<1$ such that $\mathbf{E}[e^{κ\mathbb{V}_1}]=1$, then $X_t/t^κ$ converges to some nondegenerate distribution. These results are in a way analogous to those obtained by Kesten--Kozlov--Spitzer for the transient random walk in a random environment. | |
| dc.description | Published in at http://dx.doi.org/10.1214/009117907000000123 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/math/0606411 | |
| dc.identifier | http://arxiv.org/abs/math/0606411 | |
| dc.identifier | Annals of Probability 2008, Vol. 36, No. 1, 279-318 | |
| dc.identifier | doi:10.1214/009117907000000123 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145206 | |
| dc.subject | Probability | |
| dc.subject | 60J60 (Primary) 60J55 (Secondary) | |
| dc.title | Rates of convergence of a transient diffusion in a spectrally negative Lévy potential | |
| dc.type | text |