TY - JOUR
T1 - Strong rate of convergence for the Euler–Maruyama approximation of SDEs with Hölder continuous drift coefficient
AU - Menoukeu Pamen, Olivier
AU - Taguchi, Dai
N1 - Funding Information:
The project on which this publication is based has been carried out with funding provided by the Alexander von Humboldt Foundation, under the programme financed by the German Federal Ministry of Education and Research entitled German Research Chair No. 01DG15010 and by the European Union's Seventh Framework Programme for research, technological development and demonstration under Grant Agreement No. 318984-RARE.
Publisher Copyright:
© 2016
PY - 2017/8
Y1 - 2017/8
N2 - In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) Xt=x0+∫0tb(s,Xs)ds+Lt,x0∈Rd,t∈[0,T], where the drift coefficient b:[0,T]×Rd→Rd is Hölder continuous in both time and space variables and the noise L=(Lt)0≤t≤T is a d-dimensional Lévy process. We provide the rate of convergence for the Euler–Maruyama approximation when L is a Wiener process or a truncated symmetric α-stable process with α∈(1,2). Our technique is based on the regularity of the solution to the associated Kolmogorov equation.
AB - In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) Xt=x0+∫0tb(s,Xs)ds+Lt,x0∈Rd,t∈[0,T], where the drift coefficient b:[0,T]×Rd→Rd is Hölder continuous in both time and space variables and the noise L=(Lt)0≤t≤T is a d-dimensional Lévy process. We provide the rate of convergence for the Euler–Maruyama approximation when L is a Wiener process or a truncated symmetric α-stable process with α∈(1,2). Our technique is based on the regularity of the solution to the associated Kolmogorov equation.
KW - Euler–Maruyama approximation
KW - Hölder continuous drift
KW - Rate of convergence
KW - Strong approximation
KW - Truncated symmetric α-stable
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U2 - 10.1016/j.spa.2016.11.008
DO - 10.1016/j.spa.2016.11.008
M3 - Article
AN - SCOPUS:85008168596
SN - 0304-4149
VL - 127
SP - 2542
EP - 2559
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 8
ER -