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2008 Large Deviations for One Dimensional Diffusions with a Strong Drift
Jochen Voss
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Electron. J. Probab. 13: 1479-1528 (2008). DOI: 10.1214/EJP.v13-564


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.


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Jochen Voss. "Large Deviations for One Dimensional Diffusions with a Strong Drift." Electron. J. Probab. 13 1479 - 1528, 2008.


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

zbMATH: 1193.60038
MathSciNet: MR2438814
Digital Object Identifier: 10.1214/EJP.v13-564

Primary: 60F10 60H10

Keywords: Diffusion processes , large deviations , Stochastic differential equations

Vol.13 • 2008
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