Convergence of moments in a Markov-chain central limit theorem

Convergence of Moments in a Markov-chain Central Limit Theorem

Let (Xi)1i=0 be a V -uniformly ergodic Markov chain on a general state space, and let be its stationary distribution. For g : X! R, de ne Wk(g) := k 1=2 k 1 X i=0 g(Xi) (g) : It is shown that if jgj V 1=n for a positive integer n, then ExWk(g) n converges to the n-th moment of a normal random variable with expectation 0 and variance 2 g := (g ) (g) + 1 X j=1 Z g(x)Exg(Xj) (g) 2 : This extends t...

On the Markov chain central limit theorem

The goal of this 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 th...

Convergence rates for the central limit theorem.

On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of any even order converge in the almost sure central limit theorem for martingales. A conjecture about almost sure upper bounds under wider hypotheses is formul...

A central limit theorem for functions of a Markov chain with applications to shifts