I am interested in some general theorems related to lower bounds on discrete time finite Markov chains hitting probabilities (preferably ergodic chains , but not necessarily ), with references . Similar results related to continuous time Markov chains, that allow discretization, are welcome. Thank you.



Lower bounds on discrete time finite Markov chains hitting probabilities
Chapter 10 in the book "Markov chains and mixing times (see <http://www.ams.org/publications/authors/books/postpub/mbk-107> 
 and <https://pages.uoregon.edu/dlevin/MARKOV/mcmt2e.pdf> ) is all about bounding hitting times for discrete chains.


