We study the asymptotic behavior of a diffusion process with small diffusion in a domain D. This process is reflected at ∂D with respect to a co-normal direction pointing inside D. Our asymptotic result is used to study the long time behavior of the solution of the corresponding parabolic PDE with Neumann boundary condition.
- Freidlin-Wentzell theory
- PDE with a small parameter
- diffusion process with reflection
- large deviations