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Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the maximum process

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  • Hiderah Kamal

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

Abstract

The aim of this paper is to show the approximation of Euler–Maruyama Xtn{X_{t}^{n}} for one-dimensional stochastic differential equations involving the maximum process. In addition to that it proves the strong convergence of the Euler–Maruyama whose both drift and diffusion coefficients are Lipschitz. After that, it generalizes to the non-Lipschitz case.

Suggested Citation

  • Hiderah Kamal, 2020. "Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the maximum process," Monte Carlo Methods and Applications, De Gruyter, vol. 26(1), pages 33-47, March.
    • Handle: RePEc:bpj:mcmeap:v:26:y:2020:i:1:p:33-47:n:4
    DOI: 10.1515/mcma-2020-2057
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    References listed on IDEAS

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    1. Chaumont, L. & Doney, R. A., 2000. "Some calculations for doubly perturbed Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 61-74, January.
    2. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
    3. Chan, K. S. & Stramer, O., 1998. "Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 33-44, August.
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