Donsker-Varadhan large deviations for path-distribution dependent SPDEs

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Original languageEnglish
Article number125000
Journal / PublicationJournal of Mathematical Analysis and Applications
Issue number1
Online published26 Jan 2021
Publication statusPublished - 1 Jul 2021


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.

Research Area(s)

  • Donsker-Varadhan LDP, Path-distribution dependent SDEs, Warsserstein distance