In this paper, we consider the averaging principle for a class of stochastic differential equations (SDEs) with the nonlinear terms only satisfying the local Lipschitz and monotone conditions. Compared with the classical Lipschitz and linear growth conditions, conditions given in this paper are relatively weak, so the conclusions obtained in this paper are suitable for a wider class of SDEs.

中文翻译：

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单调条件随机微分方程的平均原理

在本文中，我们考虑一类非线性项仅满足局部 Lipschitz 和单调条件的随机微分方程 (SDE) 的平均原理。与经典的 Lipschitz 和线性增长条件相比，本文给出的条件相对较弱，因此本文得出的结论适用于更广泛的 SDE 类。