Strong rate of convergence for the Euler--Maruyama scheme of SDEs with unbounded Hölder continuous drift coefficient

In this paper, we provide the strong rate of convergence for the Euler–Maruyama scheme for multi-dimensional stochastic differential equations with uniformly locally (unbounded) Hölder continuous drift and multiplicative noise. Our technique is based on Itô–Tanaka trick (Zvonkin transformation) for unbounded drift. Moreover, in order to apply the stochastic sewing lemma, we use the heat kernel estimate for the density function of the Euler–Maruyama scheme.