TY - JOUR
T1 - Semi-implicit Euler–Maruyama scheme for polynomial diffusions on the unit ball
AU - Nakagawa, Takuya
AU - Taguchi, Dai
AU - Yuasa, Tomooki
N1 - Funding Information:
The second author was supported by JSPS KAKENHI Grant Number 19K14552 . The third author was supported by JSPS KAKENHI Grant Numbers 17J05514 and 22K13965 .
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2023/3/15
Y1 - 2023/3/15
N2 - In this article, we consider numerical schemes for polynomial diffusions on the unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form 1−|x|2. We introduce a semi-implicit Euler–Maruyama scheme with the projection onto the unit ball and provide the L2-rate of convergence. The main idea to consider the numerical scheme is the transformation argument introduced by Swart [29] for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient.
AB - In this article, we consider numerical schemes for polynomial diffusions on the unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form 1−|x|2. We introduce a semi-implicit Euler–Maruyama scheme with the projection onto the unit ball and provide the L2-rate of convergence. The main idea to consider the numerical scheme is the transformation argument introduced by Swart [29] for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient.
KW - Degenerate and Hölder continuous diffusion coefficient
KW - Polynomial diffusions on the unit ball
KW - Semi-implicit Euler–Maruyama scheme
UR - http://www.scopus.com/inward/record.url?scp=85141488522&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85141488522&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2022.126829
DO - 10.1016/j.jmaa.2022.126829
M3 - Article
AN - SCOPUS:85141488522
SN - 0022-247X
VL - 519
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 126829
ER -