Averaging principle for SDEs with singular drifts driven by α-stable processes

In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with β-Hölder drift driven by α-stable processes. More specifically, we first derive the Schauder estimate for nonlocal partial differential equations (PDEs) associated with the aforementioned SDEs, within the framework of Besov-Hölder spaces. Then we consider the case where [Formula presented]. Using the Schauder estimate, we establish the strong convergence rate for the averaging principle. In particular, under suitable conditions, we obtain the optimal rate of strong convergence when [Formula presented]. Furthermore, when [Formula presented], we show the convergence of the martingale solutions of original systems to that of the averaged equation. In particular, when α∈(1,2), the drift can be a distribution.