Description
Title: A large deviation principle for discrete, possibly reducible, Markov chains.
Abstract: This talk is part of my ongoing PhD research. I will begin by presenting the subadditive method, an elegant approach for deriving large deviation principles (LDPs). This method is particularly effective for systems with strong decoupling assumptions, such as irreducible Markov chains, where it has become standard under strong recurrence conditions. However, when these assumptions are relaxed—specifically when the Markov chain is no longer irreducible—further adaptations of the method are required. I will highlight the additional challenges posed by this setting and discuss a construction that addresses them, enabling the use of the subadditive method. This construction ultimately leads to the derivation of a weak LDP for any Markov chain on a discrete state space.
