Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917271404806144 |
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| author | Czapla, Dawid Hille, Sander C. Horbacz, Katarzyna Wojewódka-Ściążko, Hanna |
| author_facet | Czapla, Dawid Hille, Sander C. Horbacz, Katarzyna Wojewódka-Ściążko, Hanna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01144 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance Czapla, Dawid Hille, Sander C. Horbacz, Katarzyna Wojewódka-Ściążko, Hanna Probability Primary: 60J25, 60F15, Secondary: 60H10, 37A30 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. |
| title | Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance |
| topic | Probability Primary: 60J25, 60F15, Secondary: 60H10, 37A30 |
| url | https://arxiv.org/abs/2507.01144 |