A Simple Stochastic Differential Equation with Discontinuous Drift
Systems and Control
2013-08-27 v1 Numerical Analysis
Abstract
In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the Euler-Maruyama method approximates a candidate density function based on the stationary Fokker-Planck equation. Furthermore, we introduce a smooth function which approximates the discontinuous drift and apply the Euler-Maruyama method and the Fokker-Planck equation with this input. The point of departure for this work is a particular SDE with discontinuous drift.
Cite
@article{arxiv.1308.5339,
title = {A Simple Stochastic Differential Equation with Discontinuous Drift},
author = {Maria Simonsen and John Leth and Henrik Schioler and Horia Cornean},
journal= {arXiv preprint arXiv:1308.5339},
year = {2013}
}
Comments
In Proceedings HAS 2013, arXiv:1308.4904