This work is mainly concerned with small noise and small time asymptotics for a class of McKean–Vlasov stochastic differential equations with local Lipschitz coefficients. We apply the modified weak convergence criteria to prove the Laplace principle (equivalently, the large deviation principle). The main results extend the existing ones to the case of fully local assumptions with respect to both the state and measure variables in the literature. As a consequence, the small time asymptotics for McKean–Vlasov SDEs are also derived.

中文翻译：

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具有局部 Lipschitz 系数的 McKean-Vlasov SDE 的小噪声和小时间渐近


这项工作主要关注一类具有局部 Lipschitz 系数的 McKean-Vlasov 随机微分方程的小噪声和小时间渐近。我们应用改进的弱收敛准则来证明拉普拉斯原理（相当于大偏差原理）。主要结果将现有的结果扩展到文献中关于状态和测度变量的完全局部假设的情况。因此，还推导出了 McKean-Vlasov SDE 的小时间渐近。