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On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients

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  • Ngo, Hoang-Long
  • Taguchi, Dai

Abstract

We consider the strong rate of convergence of the Euler–Maruyama approximation for stochastic differential equations with possibly discontinuous drift and Hölder continuous diffusion coefficient. In particular, we show that the rates obtained in some recent papers can be improved under an additional assumption that the diffusion coefficient is of bounded variation.

Suggested Citation

  • Ngo, Hoang-Long & Taguchi, Dai, 2019. "On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 102-112.
    • Handle: RePEc:eee:matcom:v:161:y:2019:i:c:p:102-112
    DOI: 10.1016/j.matcom.2019.01.012
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    References listed on IDEAS

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    1. Hashimoto, Hiroya & Tsuchiya, Takahiro, 2018. "Stability problems for Cantor stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 211-232.
    2. Kusuoka, Seiichiro, 2017. "Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 359-384.
    3. Ngo, Hoang-Long & Taguchi, Dai, 2017. "Strong convergence for the Euler–Maruyama approximation of stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 55-63.
    4. Jirô Akahori & Yuri Imamura, 2014. "On a symmetrization of diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1211-1216, July.
    5. Menoukeu Pamen, Olivier & Taguchi, Dai, 2017. "Strong rate of convergence for the Euler–Maruyama approximation of SDEs with Hölder continuous drift coefficient," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2542-2559.
    6. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
    7. Remigijus Mikulevicius & Eckhard Platen, 1991. "Rate of Convergence of the Euler Approximation for Diffusion Processes," Published Paper Series 1991-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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