Strong and weak convergence in the averaging principle for SDEs with Hölder coefficients

Abstract

Using Zvonkin's transform and the Poisson equation in $R^d$ with a parameter, we prove the averaging principle for stochastic differential equations with time-dependent Hölder continuous coefficients. Sharp convergence rates with order $(\alpha \wedge 1)/2$ in the strong sense and $(\alpha /2)\wedge 1$ in the weak sense are obtained, considerably extending the existing results in the literature. Moreover, we prove that the convergence of the multi-scale system to the effective equation depends only on the regularity of the coefficients of the equation for the slow variable, and does not depend on the regularity of the coefficients of the equation for the fast component.

References in corpus (2)

• On the Poisson equation and diffusion approximation 3
• Ergodicity of stochastic differential equations with jumps and singular coefficients

Cited by in corpus (2)

• Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations
• Diffusion approximation for fully coupled stochastic differential equations