Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 73257, 6 pages
doi:10.1155/JAMSA/2006/73257
A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient
1Department of Statistics and Actuarial Science, University of the Aegean, Karlovassi 83200, Samos, Greece
2Fachbereich Mathematik, Johann Wolfgang Goethe Universität, Frankfurt am Main 60054, Germany
Received 11 November 2004; Revised 20 September 2005; Accepted 21 September 2005
Copyright © 2006 Nikolaos Halidias and P. E. Kloeden. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The existence of a mean-square continuous strong solution is established for vector-valued Itô stochastic differential equations with a discontinuous drift coefficient, which is an increasing function, and with a Lipschitz continuous diffusion coefficient. A scalar stochastic differential equation with the Heaviside function as its drift coefficient is considered as an example. Upper and lower solutions are used in the proof.