Estimation of quadratic variation for two-parameter diffusions

In this paper we give a central limit theorem for the weighted quadratic variations process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations $\sum_{i=1}^{[n s]} \sum_{j=1}^{[n t]} | \Delta_{i,j} Y |^2$ofatwo-parameterdiffusion$Y=(Y_{(s,t)})_{(s,t)\in[0,1]^2}$observedonaregulargrid$G_n$ is an asymptotically normal estimator of the quadratic variation of $Y$ as $n$ goes to infinity.