Convergence Rate of Euler–Maruyama Scheme for SDEs with Hölder–Dini Continuous Drifts
By Jianhai Bao, Xing Huang, Chenggui Yuan. Journal of theoretical probability, 2018
60 citations recorded by the source corpus.
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 23\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{2}{3}$$\end{document} with respect to the first component and are merely Dini-continuous concerning the second component.
Subfields: Demography, Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/3bb9a129a748669a66a55a56a061da5d1c37cd66
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Citations in the corpus
- Quantifying a convergence theorem of Gyöngy and Krylov (2021, background): “In one direction, see among others [35, 37, 4, 30, 5, 10], low regularity of order α ∈ (0,1) of the drift on the Hölder scale is assumed.”