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

  • Kamal Hiderah ORCID logo EMAIL logo
Veröffentlicht/Copyright: 11. Februar 2020

Abstract

The aim of this paper is to show the approximation of Euler–Maruyama Xtn 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.

Acknowledgements

The author would like to thank the referees and the editor for the very useful comments and suggestions, which have helped to improve the paper a lot. The author is very grateful to Professor Mohsine Benabdallah for suggesting this problem, and for fruitful discussions.

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Received: 2019-08-30
Accepted: 2020-01-25
Published Online: 2020-02-11
Published in Print: 2020-03-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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