TY - JOUR
T1 - On the Euler-Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients
AU - Ngo, Hoang Long
AU - Taguchi, Dai
N1 - Funding Information:
Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number (101.03-2014.14). KOKUSAITEKI Research Fund of Ritsumeikan University and JSPS KAKENHI grant number (16J00894 to D.T.).
Publisher Copyright:
© The authors 2017.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - We study the strong rates of the Euler-Maruyama approximation for one-dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and whose diffusion coefficient is Hölder continuous. In particular, we show that the strong rate of the Euler-Maruyama approximation is 1/2 for a large class of equations whose drift is not continuous. We also provide the strong rate for equations whose drift is Hölder continuous and diffusion is nonconstant.
AB - We study the strong rates of the Euler-Maruyama approximation for one-dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and whose diffusion coefficient is Hölder continuous. In particular, we show that the strong rate of the Euler-Maruyama approximation is 1/2 for a large class of equations whose drift is not continuous. We also provide the strong rate for equations whose drift is Hölder continuous and diffusion is nonconstant.
KW - Euler-Maruyama approximation
KW - Irregular coefficients
KW - Stochastic differential equation
KW - Strong rate of convergence
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M3 - Article
AN - SCOPUS:85031719555
SN - 0272-4979
VL - 37
SP - 1864
EP - 1883
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
IS - 4
ER -