A Simple Stochastic Differential Equation with Discontinuous Drift

Maria Simonsen
John Leth
Henrik Schioler
Horia Cornean

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.

In Luca Bortolussi, Manuela L. Bujorianu and Giordano Pola: Proceedings Third International Workshop on Hybrid Autonomous Systems (HAS 2013), Rome, 17th March 2013, Electronic Proceedings in Theoretical Computer Science 124, pp. 109–123.
Published: 22nd August 2013.

ArXived at: http://dx.doi.org/10.4204/EPTCS.124.11 bibtex PDF
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