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arXiv · 1308.5339

A Simple Stochastic Differential Equation with Discontinuous Drift

Maria Simonsen·John Leth·Henrik Schioler·Horia Cornean
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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.

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Maria Simonsen, John Leth, Henrik Schioler, Horia Cornean. 2013-08-24. A Simple Stochastic Differential Equation with Discontinuous Drift. https://doi.org/10.4204/eptcs.124.11

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