Large Deviations for One Dimensional Diffusions with a Strong Drift

Information and Download

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.

Citations

I believe that this work is cited in the following text. If you know of any more citations, please let me know.

• J. Voss: Upper and Lower Bounds in Exponential Tauberian Theorems. Tbilisi Mathematical Journal, vol. 2, pp. 41–50, 2009.
  online, preprint, more…

Copyright © 2009, Jochen Voss. All content on this website (including text, pictures, and any other original works), unless otherwise noted, is licensed under a Creative Commons Attribution-Share Alike 3.0 License.