论文标题
McKean-Vlasov SDES的Onsager-Machlup动作功能
The Onsager-Machlup action functional for Mckean-Vlasov SDEs
论文作者
论文摘要
本文致力于在一类规范中得出针对McKean-Vlasov随机微分方程的Onsager-Machlup动作，这些规范主导了$ l^2（[0,1]，\ Mathbb {r}^d）$ H $ \ mathrm {\ ddot {o}} $ lder norms $ \ | \ | \ cdot \ |_α$带有$α<\ frac {1} {1} {4} $和$ l^p $ -norms，$ p> 4 $都包括在内。此外，得出了用于Onsager-Machlup动作功能的相应的Euler-Lagrange方程，并给出了一个示例。
This paper is devoted to deriving the Onsager-Machlup action functional for Mckean-Vlasov stochastic differential equations in a class of norms that dominate $L^2([0,1], \mathbb{R}^d)$, such as supremum norm $\|\cdot\|_{\infty}$, H$\mathrm{\ddot{o}}$lder norms $\|\cdot\|_α$ with $α<\frac{1}{4}$ and $L^p$-norms with $p>4$ are included. Moreover, the corresponding Euler-Lagrange equation for Onsager-Machlup action functional is derived and a example is given.
