Penalty Method for Reflected Diffusions on the Half-Line

Abstract

Consider a reflected diffusion on the positive half-line. We approximate it by solutions of stochastic differential equations using the penalty method: We emulate the "hard barrier" of reflection by a "soft barrier" of a large drift coefficient, which compells the diffusion to return to the positive half-line. The main tool of the proof is convergence of scale functions.

21 pages. Keywords: Stochastic differential equation, reflected diffusion, reflected Brownian motion, weak convergence, scale function, penalty method