On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift
Dareiotis K, Gerencser M. 2020. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 25, 82.
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Author
Dareiotis, Konstantinos;
Gerencser, MateISTA
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Abstract
The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.
Publishing Year
Date Published
2020-07-16
Journal Title
Electronic Journal of Probability
Publisher
Institute of Mathematical Statistics
Volume
25
Article Number
82
eISSN
IST-REx-ID
Cite this
Dareiotis K, Gerencser M. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 2020;25. doi:10.1214/20-EJP479
Dareiotis, K., & Gerencser, M. (2020). On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/20-EJP479
Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP479.
K. Dareiotis and M. Gerencser, “On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift,” Electronic Journal of Probability, vol. 25. Institute of Mathematical Statistics, 2020.
Dareiotis K, Gerencser M. 2020. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 25, 82.
Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal of Probability, vol. 25, 82, Institute of Mathematical Statistics, 2020, doi:10.1214/20-EJP479.
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