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Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance (2507.01144v1)
Published 1 Jul 2025 in math.PR
Abstract: In this paper, we establish the law of the iterated logarithm for a wide class of non-stationary, continuous-time Markov processes evolving on Polish spaces. Specifically, our results apply to additive functionals of processes governed by stochastically continuous Markov-Feller semigroups that exhibit exponential mixing and non-expansiveness in the Wasserstein norm, provided that a suitable moment condition on the initial distributions is satisfied.
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