| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2329 - 2348 | |
| DOI | https://doi.org/10.1051/m2an/2025061 | |
| Published online | 17 September 2025 | |
The semi-implicit euler–maruyama method for nonlinear non-autonomous stochastic differential equations driven by a class of lévy processes
1
Department of Mathematics, Shanghai Normal University, Shanghai 200234, P.R. China
2
Department of Mathematics, Jiangsu Second Normal University, Nanjing 210013, P.R. China
* Corresponding author: hjtian@shnu.edu.cn
Received:
3
November
2023
Accepted:
30
June
2025
The strong convergence of the semi-implicit Euler–Maruyama (EM) method for stochastic differential equations with nonlinear coefficients driven by a class of Lévy processes is investigated. The dependence of the convergence order of the numerical scheme on the parameters of the class of Lévy processes is discovered, which is different from existing results. In addition, the existence and uniqueness of the numerical invariant measure for the semi-implicit EM method is studied, and its convergence to the underlying invariant measure is also proved. Numerical examples are provided to confirm our theoretical results.
Mathematics Subject Classification: 60H10 / 65C30 / 60J60
Key words: Lévy process / stochastic differential equation / semi-implicit Euler–Maruyama method / strong convergence / invariant measure
© The authors. Published by EDP Sciences, SMAI 2025
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