On the Markov chain central limit theorem

@article{Jones2004OnTM,
  title={On the Markov chain central limit theorem},
  author={Galin L. Jones},
  journal={Probability Surveys},
  year={2004},
  volume={1},
  pages={299-320}
}
The goal of this expository paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains. This is done with a view towards Markov chain Monte Carlo settings and hence the focus is on the connections between drift and mixing conditions and their implications. In particular, we consider three commonly cited central limit theorems and discuss their relationship to classical results for mixing processes. Several motivating examples are… Expand
325 Citations
A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming
Spectral Theory for Weakly Reversible Markov Chains
Central limit theorem for triangular arrays of non-homogeneous Markov chains
Nonstandard Central Limit Theorems for Markov Chains
On Variance Conditions for Markov Chain CLTs
Additive Functionals for Discrete-Time Markov Chains with Applications to Birth-Death Processes
Advanced Simulation Methods Chapter 4-Elements of Markov Chains Theory
  • 2015
Modeling dependence and limit theorems for Copula-based Markov chains
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 79 REFERENCES
On the central limit theorem for geometrically ergodic Markov chains
Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo
Polynomial convergence rates of Markov chains.
General state space Markov chains and MCMC algorithms
Convergence Control Methods for Markov Chain Monte Carlo Algorithms
Polynomial ergodicity of Markov transition kernels
...
1
2
3
4
5
...