An invariance principle for the law of the iterated logarithm for some Markov chains
Bo{\l}t Witold, Majewski Adam Aleksander, Szarek Tomasz
TL;DR
This paper proves a Strassen's invariance principle for additive functionals of certain Markov chains, extending the law of the iterated logarithm to this class.
Contribution
It establishes an invariance principle for Markov chains with spectral gap in Wasserstein metric, a novel extension of classical results.
Findings
Proves Strassen's invariance principle for specific Markov chains.
Extends the law of the iterated logarithm to additive functionals.
Uses spectral gap in Wasserstein metric as key condition.
Abstract
The Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Geometric Analysis and Curvature Flows · Point processes and geometric inequalities