TY  - INPR
A1  - Lê, Khoa
A1  - Ling, Chengcheng
T1  - Taming singular stochastic differential equations: a numerical method
T2  - arXiv
N2  - 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. The result is then applied to provide numerical solutions for stochastic transport equations with singular vector fields satisfying the aforementioned condition.
Y1  - 2023
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/108670
IS  - arXiv:2110.01343
ER  -