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

Guo, Qian and Liu, Wei and Mao, Xuerong and Yue, Rongxian (2017) The partially truncated Euler-Maruyama method and its stability and boundedness. Applied Numerical Mathematics. ISSN 0168-9274 (In Press)

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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.