On Functional CLT for Reversible Markov Chains with nonlinear growth of the Variance
Probability
2013-05-10 v3 Statistics Theory
Statistics Theory
Abstract
In this paper we study the functional central limit theorem for stationary Markov chains with self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n; and establish that conditional convergence in distribution of partial sums implies functional CLT. The main tools are maximal inequalities that are further exploited to derive conditions for tightness and convergence to the Brownian motion.
Keywords
Cite
@article{arxiv.1112.2751,
title = {On Functional CLT for Reversible Markov Chains with nonlinear growth of the Variance},
author = {Martial Longla and Costel Peligrad and Magda Peligrad},
journal= {arXiv preprint arXiv:1112.2751},
year = {2013}
}
Comments
20 pages, Functional CLT, Reversible Markov chains, Metropolis-Hastings