On Functional CLT for Reversible Markov Chains with nonlinear growth of the Variance

Details On Functional CLT for Reversible Markov Chains with nonlinear growth of the Variance On Functional CLT for Reversible Markov Chains with nonlinear growth of the Variance

2011-12-13

arxiv.org/abs/1112.2751v1

Mathematics

Probability

20 pages, Functional CLT, Reversible Markov chains, Metropolis-Hastings

Scientific paper

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.

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