Large Deviations for One Dimensional Diffusions with a Strong Drift

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details: : Large Deviations for One Dimensional Diffusions with a Strong Drift. Electronic Journal of Probability, vol. 13, no. 53, pp. 1479–1526, 2008.
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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.

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