Electronic Journal of Probability

Large Deviations for One Dimensional Diffusions with a Strong Drift

Jochen Voss

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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 $\theta b$ where $b$ is a drift function and $\theta$ a real number, when $\theta$ converges to $\infty$. 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.

Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 53, 1479-1528.

Dates
Accepted: 1 September 2008
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819126

Digital Object Identifier
doi:10.1214/EJP.v13-564

Mathematical Reviews number (MathSciNet)
MR2438814

Zentralblatt MATH identifier
1193.60038

Subjects
Primary: 60F10 60H10

Keywords
large deviations diffusion processes stochastic differential equations

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Voss, Jochen. Large Deviations for One Dimensional Diffusions with a Strong Drift. Electron. J. Probab. 13 (2008), paper no. 53, 1479--1528. doi:10.1214/EJP.v13-564. https://projecteuclid.org/euclid.ejp/1464819126


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