Limit Theorems for quadratic forms of Markov Chains
  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. 
Yves F. Atchade and Matias D. Cattaneo
math.PR