Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms

11/08/2021

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by   Tuan-Anh Nguyen, et al.

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Classical approximation results for stochastic differential equations analyze the L^p-distance between the exact solution and its Euler-Maruyama approximations. In this article we measure the error with temporal-spatial Hölder-norms. Our motivation for this are multigrid approximations of the exact solution viewed as a function of the starting point. We establish the classical strong convergence rate 0.5 with respect to temporal-spatial Hölder-norms if the coefficient functions have bounded derivatives of first and second order.