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Convergence rate of the EM algorithm for SDEs with low regular drifts

Part of: Stochastic analysis Functional-differential and differential-difference equations

Published online by Cambridge University Press:  14 February 2022

Jianhai Bao ,
Xing Huang  and
Shao-Qin Zhang
Jianhai Bao*
Affiliation:
Tianjin University
Xing Huang*
Affiliation:
Tianjin University
Shao-Qin Zhang*
Affiliation:
Central University of Finance and Economics
*
*Postal address: Center for Applied Mathematics, Tianjin University, Tianjin 300072, China.
*Postal address: Center for Applied Mathematics, Tianjin University, Tianjin 300072, China.
****Postal address: School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China. Email address: zhangsq@cufe.edu.cn
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Abstract

In this paper we employ a Gaussian-type heat kernel estimate to establish Krylov’s estimate and Khasminskii’s estimate for the Euler–Maruyama (EM) algorithm. For applications, by taking Zvonkin’s transformation into account, we investigate the convergence rate of the EM algorithm for a class of multidimensional stochastic differential equations (SDEs) with low regular drifts, which need not be piecewise Lipschitz.

Keywords

Zvonkin’s transformEuler–Maruyama approximationlow regular driftKrylov’s estimate

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 34K26: Singular perturbations 39B72: Systems of functional equations and inequalities

Information

Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 2 , June 2022 , pp. 447 - 470
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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