Limit Theorems for quadratic forms of Markov Chains

Details Limit Theorems for quadratic forms of Markov Chains Limit Theorems for quadratic forms of Markov Chains

2011-08-13

arxiv.org/abs/1108.2743v1

Mathematics

Probability

22 pages, 2 figures

Scientific paper

We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results to Markov Chain Monte Carlo simulation. As another illustration, we use the method to derive a central limit theorem for U-statistics with varying kernels.

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