Convergence rate of EM scheme for $\text {\normalfont SDDEs}$
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- by Jianhai Bao and Chenggui Yuan PDF
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Abstract:
In this paper we investigate the convergence rate of the Euler-Maruyama (EM) scheme for a class of stochastic differential delay equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In particular, we reveal that the convergence rate of the Euler-Maruyama scheme is $\frac {1}{2}$ for the Brownian motion case, while we show that it is best to use the mean-square convergence for the pure-jump case and that the order of mean-square convergence is close to $\frac {1}{2}$.References
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Additional Information
- Jianhai Bao
- Affiliation: Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom
- Email: majb@swansea.ac.uk
- Chenggui Yuan
- Affiliation: Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom
- Email: C.Yuan@swansea.ac.uk
- Received by editor(s): November 17, 2011
- Published electronically: May 13, 2013
- Communicated by: Edward C. Waymire
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3231-3243
- MSC (2010): Primary 65C30; Secondary 60H10, 65L20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11886-1
- MathSciNet review: 3068976