## Electronic Journal of Probability

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

### Large Deviations for One Dimensional Diffusions with a Strong Drift

#### 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