The modified truncated Euler-Maruyama method for stochastic differential equations with concave diffusion coefficients

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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 languageEnglish
Article number115660
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume440
Early online date6 Nov 2023
DOIs
Publication statusPublished - 30 Apr 2024

Keywords

  • stochastic differential equation
  • truncated Euler–Maruyama method
  • concave diffusion coefficient

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