Author

Austin Brown

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Preprint Sep 2026

Markov Chain CLTs: Resolving Open Problems

Markov chain central limit theorems (CLTs) and their associated variances are very important for implementing Markov chain Monte Carlo algorithms among other applications. H\"aggstr\"om and Rosenthal (2007) presented various results regarding the equality of different formulae for this variance and also posed seven ope...

Austin Brown, Jeffrey S. Rosenthal, Quan Zhou · 0 citations

Preprint Aug 2026

Hyper-V uniform ergodicity of Markov chains

We develop a new uniform drift condition and local minorization that implies a stronger weighted form of uniform ergodicity for Markov chains we call hyper-V uniform ergodicity. The convergence guarantees geometric decay of the bias towards the invariant measure independently of the initialization for all functions con...

Austin Brown, K. Khare · 0 citations