Donsker-Varadhan large deviations for path-distribution dependent SPDEs

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 not standard 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.