Convergence of Moments in a Markov-chain central limit theorem

July, 2001
Report Number: 
598
Authors: 
D. Steinsaltz
Citation: 
PDf
Abstract: 

We show that all moments of the partial sum process of a test function g along the paths of a V-uniformly ergodic Markov chain converge to the corresponding moments of a normal variable. For the n-th moment to converge, g^n must be bounded by a constant times V. We also derive starting-point dependent bounds on the rate of convergence.

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