Strong approximation for additive functionals of geometrically ergodic Markov chains

DOI10.1214/EJP.V20-3746zbMath1327.60085MaRDI QIDQ2515879

Emmanuel Rio, Florence Merlevède

Publication date: 7 August 2015

Published in: Electronic Journal of Probability (Search for Journal in Brave)

zbMATH Keywords

additive functionalsinvariance principlepartial sumsrenewal processesstrong mixingstrong approximationabsolute regularitygeometrically ergodic Markov chains

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Strong limit theorems (60F15) Markov renewal processes, semi-Markov processes (60K15) Functional limit theorems; invariance principles (60F17) Local time and additive functionals (60J55)

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Strong Gaussian approximation for cumulative processes ⋮ Strong Gaussian approximation of metastable density-dependent Markov chains on large time scales ⋮ A heavy-traffic perspective on departure process variability ⋮ Strong invariance principles for ergodic Markov processes ⋮ Rates in almost sure invariance principle for slowly mixing dynamical systems ⋮ Rates in almost sure invariance principle for dynamical systems with some hyperbolicity ⋮ An alternative to the coupling of Berkes-Liu-Wu for strong approximations ⋮ Rates in almost sure invariance principle for quickly mixing dynamical systems ⋮ General Bernstein-like inequality for additive functionals of Markov chains

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