The Freidlin-Wentzell LDP with rapidly growing coefficients

Details The Freidlin-Wentzell LDP with rapidly growing coefficients The Freidlin-Wentzell LDP with rapidly growing coefficients

2006-05-14

arxiv.org/abs/math/0605365v1

Stochastic Differential Equations:Theory and Applications, a volume in honor of B.L Rozovskii (2007) World Scientific Publishi

Mathematics

Probability

20 pages

Scientific paper

The Large Deviations Principle (LDP) is verified for a homogeneous diffusion process with respect to a Brownian motion $B_t$, $$ X^\eps_t=x_0+\int_0^tb(X^\eps_s)ds+ \eps\int_0^t\sigma(X^\eps_s)dB_s, $$ where $b(x)$ and $\sigma(x)$ are are locally Lipschitz functions with super linear growth. We assume that the drift is directed towards the origin and the growth rates of the drift and diffusion terms are properly balanced. Nonsingularity of $a=\sigma\sigma^*(x)$ is not required.

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