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arXiv · 1907.09256

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

Michael Röckner·Xiaobin Sun·Longjie Xie
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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 $(α\wedge1)/2$ in the strong sense and $(α/2)\wedge1$ 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.

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Michael Röckner, Xiaobin Sun, Longjie Xie. 2019-07-22. Strong and weak convergence in the averaging principle for SDEs with Hölder coefficients. https://arxiv.org/abs/1907.09256

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