Penalty Method for Reflected Diffusions on the Half-Line

TL;DR

This paper introduces a penalty method to approximate reflected diffusions on the half-line by using stochastic differential equations with large drift coefficients to emulate reflection.

Contribution

It provides a novel approach to approximate reflected diffusions via a penalty method and proves convergence using scale functions.

Findings

Successful approximation of reflected diffusions using the penalty method

Convergence established through analysis of scale functions

Method offers a practical way to simulate reflected diffusions

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.