Large deviation principle for the diffusion-transmutation processes and dirichlet problem for PDE systems with small parameter

Summary The diffusion-transmutation processes are considered as the diffusivities are of order ,0 and the transmutation intensities are of order ^–1. We prove a large deviation principle for the position joint with the type occupation times as 0 and study the exit problem for this process. We consider the Levinson case where a trajectory of the average drift field exits from a domain in finite time in a regular way and the large deviation case where the average drift field on the boundary points inward at the domain. The exit place and the type distribution at the exit time are determined as 0; this gives the limit of the Dirichlet problems for the corresponding PDE systems with a parameter 0.Supported in part by ARO Grant DAAL03-92-G0219Supported in part by NSF DMS9207928