  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.
