Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance

Dawid Czapla; Sander C. Hille; Katarzyna Horbacz; Hanna Wojewódka-Ściążko

doi:10.1016/j.jde.2026.114220

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arXiv · 2507.01144

Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance

Dawid Czapla·Sander C. Hille·Katarzyna Horbacz·Hanna Wojewódka-Ściążko

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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 result applies to certain additive functionals of processes governed by stochastically continuous Markov-Feller semigroups that exhibit exponential mixing and non-expansiveness in the Wasserstein distance, provided that a suitable moment condition involving the initial distribution is satisfied. Furthermore, we outline the application of this result to a Markov process arising as the solution of an infinite-dimensional stochastic differential equation with dissipative drift and additive noise.

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BibTeX RIS

Dawid Czapla, Sander C. Hille, Katarzyna Horbacz, Hanna Wojewódka-Ściążko. 2025-07-01. Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance. https://doi.org/10.1016/j.jde.2026.114220

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