Donsker-Varadhan Large Deviations for Path-Distribution Dependent SPDEs
Probability
2020-02-21 v1
Abstract
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.
Cite
@article{arxiv.2002.08652,
title = {Donsker-Varadhan Large Deviations for Path-Distribution Dependent SPDEs},
author = {Panpan Ren and Feng-Yu Wang},
journal= {arXiv preprint arXiv:2002.08652},
year = {2020}
}
Comments
32 pages