Convergence Rate of Euler–Maruyama Scheme for SDEs with Hölder–Dini Continuous Drifts

Jianhai Bao (), Xing Huang () and Chenggui Yuan ()
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Jianhai Bao: Swansea University
Xing Huang: Tianjin University
Chenggui Yuan: Swansea University

Journal of Theoretical Probability, 2019, vol. 32, issue 2, 848-871

Abstract: Abstract In this paper, we are concerned with convergence rate of Euler–Maruyama scheme for stochastic differential equations with Hölder–Dini continuous drifts. The key contributions are as follows: (i) by means of regularity of non-degenerate Kolmogrov equation, we investigate convergence rate of Euler–Maruyama scheme for a class of stochastic differential equations which allow the drifts to be Dini continuous and unbounded; (ii) by the aid of regularization properties of degenerate Kolmogrov equation, we discuss convergence rate of Euler–Maruyama scheme for a range of degenerate stochastic differential equations where the drifts are Hölder–Dini continuous of order $$\frac{2}{3}$$ 2 3 with respect to the first component and are merely Dini-continuous concerning the second component.

Keywords: Euler–Maruyama scheme; Convergence rate; Hölder–Dini continuity; Degenerate stochastic differential equation; Kolmogorov equation; 60H35; 41A25; 60H10 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-018-0854-9

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