Taming singular stochastic differential equations: A numerical method

10/04/2021

∙

by   Khoa Le, et al.

∙

0

∙

share

We consider a generic and explicit tamed Euler–Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusion coefficient is uniformly elliptic, Hölder continuous and weakly differentiable in the spatial variables while the drift satisfies the Ladyzhenskaya–Prodi–Serrin condition, as considered by Krylov and Röckner (2005). In the discrete scheme, the drift is tamed by replacing it by an approximation. A strong rate of convergence of the scheme is provided in terms of the approximation error of the drift in a suitable and possibly very weak topology. A few examples of approximating drifts are discussed in detail. The parameters of the approximating drifts can vary and be fine-tuned to achieve the standard 1/2-strong convergence rate with a logarithmic factor.