On Large Deviations for a Multidimensional Random Process with Slow and Fast Diffusities

#### S.C. Carmona

1998, v.4, №4, 431-463

ABSTRACT

We establish a Large Deviation Principle (LDP) for a family of multidimensional diffusion processes depending on a small parameter $\epsilon > 0$. The diffusion matrix is non-homogeneous depending on $x \in \r^r$ and $y \in [-b,b]$; the diffusities are of order $\epsilon$ in $x$-direction and of order $1/ \epsilon$ in $y$-direction. The motivation of the present paper is the asymptotic analysis, as $\epsilon \downarrow 0$, of a nonlinear initial-boundary value problem via Freidlin - Wentzell's probabilistic method.

Keywords: diffusion,large deviations,Markov process,Feynman - Kac formula,fast motion,slow motion