Estimation of quadratic variation for two-parameter diffusions

In this paper we give a central limit theorem for the weighted quadratic variation process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations ∑i=1[ns]∑j=1[nt]|Δi,jY|2 of a two-parameter diffusion Y=(Y(s,t))(s,t)∈[0,1]2Y=(Y(s,t))(s,t)∈[0,1]2 observed on a regular grid GnGn form an asymptotically normal estimator of the quadratic variation of YY as nn goes to infinity.