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

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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. Milošević, Marija, 2022. "Stochastic serotonin model with discontinuous drift," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 359-374.
    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. 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.

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