Large Deviations for One Dimensional Diffusions with a Strong Drift
Jochen Voss, University of Warwick
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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