Convergence Rate of Euler-Maruyama Scheme for SDEs with Rough Coefficients

Abstract

In this paper, we are concerned with convergence rate of Euler-Maruyama scheme for stochastic differential equations with rough coefficients. The key contributions lie in (i), by means of regularity of non-degenerate Kolmogrov equation, we investigate convergence rate of Euler-Maruyama scheme for a class of stochastic differential equations, which allow the drifts to be Dini-continuous and unbounded; (ii) by the aid of regularization properties of degenerate Kolmogrov equation, we discuss convergence rate of Euler-Maruyama scheme for a range of degenerate stochastic differential equations, where the drift is locally Hölder-Dini continuous of order $\frac{2}{3}$ with respect to the first component, and is merely Dini-continuous concerning the second component.

20 pages

References in corpus (1)

• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient

Cited by in corpus (1)

• Approximation of SPDEs with Holder Continuous Drifts