Abstract
Influenced by Gyöngy and Rásonyi (2011), many scholars established the strong convergence of several numerical methods for scalar stochastic differential equations (SDEs) with superlinearly growing drift and Hölder continuous diffusion coefficients. However, their methods depend on the Yamada-Watanabe method and therefore fail to work for multi-dimensional SDEs. In this paper, we study the strong Lp−convergence, for all p ⩾ 2, of the modified truncated Euler–Maruyama method for multi-dimensional SDEs with superlinearly growing drift and concave diffusion coefficients satisfying the Osgood condition. We also discuss an example with computer simulations to illustrate our theoretical results.
Original language | English |
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Article number | 115660 |
Number of pages | 13 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 440 |
Early online date | 6 Nov 2023 |
DOIs | |
Publication status | Published - 30 Apr 2024 |
Keywords
- stochastic differential equation
- truncated Euler–Maruyama method
- concave diffusion coefficient