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

Yang, Hao and Wu, Fuke and Kloeden, Peter E. and Mao, Xuerong (2020) The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients. Journal of Computational and Applied Mathematics, 366. 112379. ISSN 0377-0427

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    Abstract

    In stochastic financial and biological models, the diffusion coefficients often involve the term √x, or more general |x|r for r ∈ (0,1), which is non-Lipschitz. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) approximation first proposed by Mao (2015) for one-dimensional stochastic differential equations (SDEs) with superlinearly growing drifts and the Hölder continuous diffusion coefficients.