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 $\sum_{ i=1}^{ [n s]} \sum_{ j=1}^{ [n t]} | \Delta_{ i,j} Y |^2$ of a two-parameter diffusion $Y=(Y_{ (s,t)})_{ (s,t)\in[0,1]^2}$ observed on a regular grid $G_n$ is an asymptotically normal estimator of the quadratic variation of $Y$ as $n$ goes to infinity.
Categories: math.PR math.ST stat.TH