A useful version of the central limit theorem for a general class of Markov chains

DOI10.1016/j.jmaa.2019.123725zbMath1432.60033arXiv1804.09220OpenAlexW2893788374WikidataQ126647440 ScholiaQ126647440MaRDI QIDQ2287316

Dawid Czapla, Katarzyna Horbacz, Hanna Wojewódka-Ściążko

Publication date: 20 January 2020

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.09220

zbMATH Keywords

Markov chaincentral limit theoremrandom dynamical systemasymptotic coupling

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (8)

The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm ⋮ Limit theorems of additive functionals for regime-switching diffusions with infinite delay ⋮ On absolute continuity of invariant measures associated with a piecewise-deterministic Markov process with random switching between flows ⋮ Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process ⋮ Limit theorems for additive functionals of stochastic functional differential equations with infinite delay ⋮ Exponential ergodicity in the bounded-Lipschitz distance for some piecewise-deterministic Markov processes with random switching between flows ⋮ The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations ⋮ The Strassen invariance principle for certain non-stationary Markov–Feller chains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Law of large numbers for random dynamical systems
• Limit theorems for some Markov chains
• The central limit theorem for random dynamical systems
• Central limit theorem for Markov processes with spectral gap in the Wasserstein metric
• Existence of a unique invariant measure for a class of equicontinuous Markov operators with application to a stochastic model for an autoregulated gene
• Markov chains and stochastic stability
• Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations
• Law of large numbers and central limit theorem for randomly forced PDE's
• A criterion on asymptotic stability for partially equicontinuous Markov operators
• Exponential mixing properties of stochastic PDEs through asymptotic coupling
• Central limit theorems for additive functionals of Markov chains.
• Exponential convergence for Markov systems
• Exponential rate of convergence for some Markov operators
• Dynamic Behavior of Stochastic Gene Expression Models in the Presence of Bursting
• Central Limit Theorem for some non-stationary Markov chains
• Exponential ergodicity of some Markov dynamical systems with application to a Poisson-driven stochastic differential equation
• Random iteration with place dependent probabilities
• Fluctuations in Markov Processes

This page was built for publication: A useful version of the central limit theorem for a general class of Markov chains