论文标题
Donsker-Varadhan大偏差，用于依赖路径分布的SPDE
Donsker-Varadhan Large Deviations for Path-Distribution Dependent SPDEs
论文作者
论文摘要
作为表征马尔可夫过程长期行为的重要工具，Donsker-Varadhan LDP（大偏差原理）不直接适用于分布依赖的SDE/SPDES，因为该解决方案是非马克维亚的。我们为分布依赖的SDE/SPDE的几种不同模型建立了这种类型的LDP，这些模型也可能与记忆一起通过将原始方程与相应的分布独立的方程进行比较。作为准备工作，还研究了应对路径分布的依赖性SPDE的存在，唯一性和指数收敛性，这本身应该很有趣。
As an important tool characterizing the long time behavior of Markov processes, the Donsker-Varadhan LDP (large deviation principle) does not directly apply to distribution dependent SDEs/SPDEs since the solutions are non-Markovian. We establish this type LDP for several different models of distribution dependent SDEs/SPDEs which may also with memories, by comparing the original equations with the corresponding distribution independent ones. As preparations, the existence, uniqueness and exponential convergence are also investigated for path-distribution dependent SPDEs which should be interesting by themselves.
