Convergence rate and stability of the truncated Euler-Maruyama method for stochastic differential equations

Liangjian Hu, Xiaoyue Li, Xuerong Mao

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9 Citations (Scopus)
27 Downloads (Pure)

Abstract

Recently, Mao [13] developed a new explicit method, called the truncated Euler- Maruyama (EM) method, for the nonlinear SDE and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. In his another follow-up paper [14], he discussed the rates of Lq -convergence of the truncated EM method for q ≥ 2 and showed that the order of Lq-convergence can be arbitrarily close to q/2 under some additional conditions. However, there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is to establish the convergence rate without these restrictions. The other aim is to study the stability of the truncated EM method. The advantages of our new results will be highlighted by the comparisons with the results in [13, 14] as well as others on the tamed EM and implicit methods.
Original languageEnglish
Pages (from-to)274-289
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume337
Early online date31 Jan 2018
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

  • stochastic differential equation
  • Khasminskii-type condition
  • truncated Euler-Maruyama method
  • convergence rate
  • stability

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  • Projects

    Epsrc Doctoral Training Grant | Liang, Yanfeng

    Greenhalgh, D., Mao, X. & Liang, Y.

    EPSRC (Engineering and Physical Sciences Research Council)

    1/10/123/10/16

    Project: Research Studentship - Internally Allocated

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