The partially truncated Euler-Maruyama method and its stability and boundedness

Qian Guo, Wei Liu, Xuerong Mao, Rongxian Yue

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Abstract

The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will not
only establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by
showing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.
Original languageEnglish
JournalApplied Numerical Mathematics
Publication statusAccepted/In press - 23 Jan 2017

Keywords

  • Stochastic differential equations
  • local Lipschitz condition
  • Khasminskii-type condition
  • partially truncated Euler-Maruyama method
  • stability
  • boundedness

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