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Léo Daures

Publications and source records attributed to Léo Daures.

2 recordsLinked to original sources
arXiv2026

Large deviations for possibly reducible Markov chains on discrete state spaces

We study the large deviations of Markov chains under the sole assumption that the state space is discrete. In particular, we do not require any of the usual irreducibility and exponential tightness assumptions. Using subadditive arguments, we provide an elementary and self-contained proof of the level-2 and level-3 large deviation principles. Due to the possible reducibility of the Markov chain, the rate functions may be nonconvex and may differ, outside a specific set, from the Donsker-Varadhan entropy and other classical rate functions.

math.PR↗
arXiv2026

Large deviations for non-irreducible Markov chains on Euclidean spaces

We establish the weak large deviations principle for empirical measures of Markov chains on $\mathbb R^d$ under mild assumptions. In particular, no irreducibility is assumed and the initial measure may be arbitrary. The proof is entirely self-contained and relies on subadditivity. In the absence of irreducibility, examples show that the rate function is not convex in general.

math.PR↗