论文标题
McKean-Vlasov SDES的大而中等的偏差原理
Large and moderate deviation principles for McKean-Vlasov SDEs with jumps
论文作者
论文摘要
在本文中，我们认为McKean-Vlasov随机微分方程（MVSDE）由Lévy噪声驱动。通过识别MVSDES解决方案所满足的正确方程，并以移动的驾驶噪声来确定一个框架，以完全应用弱收敛方法来建立MVSDES的较大且中等的偏差原理。在普通SDE的情况下，使用相应的骨架方程的解简单地通过Cameron-Martin空间的元素代替噪声来计算速率函数。事实证明，MVSDE的正确速率函数是通过骨架方程的解决方案来定义的，通过平滑函数代替噪声并通过相应确定性方程的解（无噪声）的解决方案的分布来代替方程中涉及的分布。这有些令人惊讶。通过这种方法，与现有文献相比，我们获得了更广泛的MVSDE类别的大型和中等偏差原则。
In this paper, we consider McKean-Vlasov stochastic differential equations (MVSDEs) driven by Lévy noise. By identifying the right equations satisfied by the solutions of the MVSDEs with shifted driving Lévy noise, we build up a framework to fully apply the weak convergence method to establish large and moderate deviation principles for MVSDEs. In the case of ordinary SDEs, the rate function is calculated by using the solutions of the corresponding skeleton equations simply replacing the noise by the elements of the Cameron-Martin space. It turns out that the correct rate function for MVSDEs is defined through the solutions of skeleton equations replacing the noise by smooth functions and replacing the distributions involved in the equation by the distribution of the solution of the corresponding deterministic equation (without the noise). This is somehow surprising. With this approach, we obtain large and moderate deviation principles for much wider classes of MVSDEs in comparison with the existing literature.
