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

Author

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  • Nikolaos Halidias
  • P. E. Kloeden

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.

Suggested Citation

  • Nikolaos Halidias & P. E. Kloeden, 2006. "A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-6, May.
    • Handle: RePEc:hin:jnijsa:073257
    DOI: 10.1155/JAMSA/2006/73257
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    Cited by:

    1. Mark Podolskij & Bezirgen Veliyev & Nakahiro Yoshida, 2018. "Edgeworth expansion for Euler approximation of continuous diffusion processes," CREATES Research Papers 2018-28, Department of Economics and Business Economics, Aarhus University.
    2. Przybyłowicz, Paweł & Szölgyenyi, Michaela, 2021. "Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    3. Milošević, Marija, 2022. "Stochastic serotonin model with discontinuous drift," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 359-374.

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