Exact sampling of diffusions with a discontinuity in the drift

TL;DR

This paper presents exact simulation methods for one-dimensional diffusions with discontinuous drift, utilizing retrospective rejection sampling and Brownian motion properties to generate accurate sample paths.

Contribution

It introduces novel exact sampling algorithms for diffusions with discontinuous drift, expanding simulation capabilities beyond smooth cases.

Findings

Effective exact sampling algorithms demonstrated

Simulation accuracy validated with illustrative example

Applicable to diffusions with complex drift discontinuities

Abstract

We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws related to those of Brownian motion and its local time and are based on the principle of retrospective rejection sampling. A simple illustration is provided.