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Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients


Authors: Hoang-Long Ngo and Dai Taguchi
Journal: Math. Comp. 85 (2016), 1793-1819
MSC (2010): Primary 60H35, 41A25, 60H10, 65C30
DOI: https://doi.org/10.1090/mcom3042
Published electronically: October 30, 2015
MathSciNet review: 3471108
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Abstract: We consider the Euler-Maruyama approximation for multi-dimen-
sional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is Hölder continuous and uniformly elliptic.


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Additional Information

Hoang-Long Ngo
Affiliation: Department of Mathematics and Informatics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
Email: ngolong@hnue.edu.vn

Dai Taguchi
Affiliation: Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577, Japan
Email: dai.taguchi.dai@gmail.com

DOI: https://doi.org/10.1090/mcom3042
Keywords: Euler-Maruyama approximation, strong approximation, rate of convergence, stochastic differential equation, irregular coefficient
Received by editor(s): November 10, 2013
Received by editor(s) in revised form: April 10, 2014, July 6, 2014, October 16, 2014, and January 24, 2015
Published electronically: October 30, 2015
Additional Notes: This research was supported by grants of the Japanese government.
Article copyright: © Copyright 2015 American Mathematical Society