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A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient

Nikolaos Halidias and P. E. Kloeden

International Journal of Stochastic Analysis, 2006, vol. 2006, 1-6


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.

Date: 2006
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DOI: 10.1155/JAMSA/2006/73257

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