Random perturbations of dynamical systems with reflecting boundary and corresponding PDE with a small parameter

Article type: Research Article

Authors: Hu, Wenqing | Tcheuko, Lucas^;

Affiliations: Department of Mathematics, University of Maryland at College Park, College Park, MD, USA. E-mails: {huwenqing, lucast}@math.umd.edu

Note: [] Corresponding author. E-mail: lucast@math.umd.edu

Abstract: 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.

Keywords: PDE with a small parameter, large deviations, Freidlin–Wentzell theory, diffusion process with reflection

DOI: 10.3233/ASY-141217

Journal: Asymptotic Analysis, vol. 88, no. 4, pp. 187-200, 2014