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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convergence rate of EM scheme for SDDEs


Authors: Jianhai Bao and Chenggui Yuan
Journal: Proc. Amer. Math. Soc. 141 (2013), 3231-3243
MSC (2010): Primary 65C30; Secondary 60H10, 65L20
Published electronically: May 13, 2013
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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}$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11886-1
PII: S 0002-9939(2013)11886-1
Keywords: Stochastic differential delay equation, highly nonlinear, jumps, EM scheme, convergence rate
Received by editor(s): November 17, 2011
Published electronically: May 13, 2013
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.