Large Deviations for One Dimensional Diffusions with a Strong Drift
Information and Download
| details: | Voss, Jochen: Large Deviations for One Dimensional Diffusions with a Strong Drift. Electronic Journal of Probability, vol. 13, no. 53, pp. 1479–1526, 2008. |
|---|---|
| preprint: | preprint:pdf , preprint:ps |
| link: | http://www.math.washington.edu/ ejpecp/viewarticle.php?id=1864 |
| metadata: | BibTeX, MathSciNet, Google |
| keywords: | large deviations, diffusion processes, SDEs |
| MSC2000: | 60F10 , 60H10 |
Abstract
We derive a large deviation principle which describes the behaviour of a diffusion process with additive noise under the influence of a strong drift. Our main result is a large deviation theorem for the distribution of the end-point of a one-dimensional diffusion with drift θb where b is a drift function and θ a real number, when θ converges to ∞. It transpires that the problem is governed by a rate function which consists of two parts: one contribution comes from the Freidlin-Wentzell theorem whereas a second term reflects the cost for a Brownian motion to stay near a equilibrium point of the drift over long periods of time.
Copyright © 2008 Jochen Voss. All content on this website (including text, pictures, and any other original works), unless otherwise noted, is licensed under the CC BY-SA 4.0 license.