TY - JOUR
T1 - On the strong convergence rate for the Euler–Maruyama scheme of one-dimensional SDEs with irregular diffusion coefficient and local time
AU - Taguchi, Dai
N1 - Funding Information:
The author would like to thank an anonymous referee for his/her careful readings and comments. The author was supported by JSPS KAKENHI Grant Number 19K14552 .
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022
Y1 - 2022
N2 - The strong rate of convergence for the Euler–Maruyama scheme of stochastic differential equations (SDEs) driven by a Brownian motion with Hölder continuous diffusion coefficient or irregular drift coefficient have been widely studied. In the case of irregular diffusion coefficient, however, there are few studies. In this article, under Le Gall's condition on the diffusion coefficient, which leads to conclude the pathwise uniqueness for SDEs, we provide the same result on the strong rate of convergence as in the case of 1/2-Hölder continuous diffusion coefficient. The idea of the proof is to use a version of Avikainen's inequality. As an application, we introduce a numerical scheme for SDEs with local time.
AB - The strong rate of convergence for the Euler–Maruyama scheme of stochastic differential equations (SDEs) driven by a Brownian motion with Hölder continuous diffusion coefficient or irregular drift coefficient have been widely studied. In the case of irregular diffusion coefficient, however, there are few studies. In this article, under Le Gall's condition on the diffusion coefficient, which leads to conclude the pathwise uniqueness for SDEs, we provide the same result on the strong rate of convergence as in the case of 1/2-Hölder continuous diffusion coefficient. The idea of the proof is to use a version of Avikainen's inequality. As an application, we introduce a numerical scheme for SDEs with local time.
KW - Avikainen's inequality
KW - Euler–Maruyama scheme
KW - Irregular diffusion coefficient
KW - Rate of convergence
KW - SDEs with local time
KW - Stochastic differential equation
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U2 - 10.1016/j.jco.2022.101695
DO - 10.1016/j.jco.2022.101695
M3 - Article
AN - SCOPUS:85134150098
JO - Journal of Complexity
JF - Journal of Complexity
SN - 0885-064X
M1 - 101695
ER -