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The aim of this paper is to show the approximation of Euler–MaruyamaX  t  n{X_{t}^{n}}    for one-dimensional stochastic differential equations involving the maximum process. In addition to that it proves the strong convergence of the Euler–Maruyama whose both drift and diffusion coefficients are Lipschitz. After that, it generalizes to the non-Lipschitz case.

Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the maximum process