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Strong rate of convergence for the Euler–Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero

Author

Listed:
  • Benabdallah Mohsine

    (Department of Mathematics, Faculty of Science, University of Ibn Tofail, Kenitra, Morocco)

  • Hiderah Kamal

    (Department of Mathematics, Faculty of Science, University of Aden, Aden, Yemen)

Abstract

We present the Euler–Maruyama approximation for one-dimensional stochastic differential equations involving the local time at point zero. Also, we prove the strong convergence of the Euler–Maruyama approximation whose both drift and diffusion coefficients are Lipschitz. After that, we generalize to the non-Lipschitz case.

Suggested Citation

  • Benabdallah Mohsine & Hiderah Kamal, 2018. "Strong rate of convergence for the Euler–Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 249-262, December.
    • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:4:p:249-262:n:2
    DOI: 10.1515/mcma-2018-2021
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    References listed on IDEAS

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    1. Qing Li & Yanli Zhou & Xinquan Zhao & Xiangyu Ge, 2014. "Fractional Order Stochastic Differential Equation with Application in European Option Pricing," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-12, August.
    2. Blei, Stefan & Engelbert, Hans-Jürgen, 2013. "One-dimensional stochastic differential equations with generalized and singular drift," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4337-4372.
    3. Étoré, Pierre & Martinez, Miguel, 2018. "Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2642-2687.
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