2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146297In 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 $\sum_{i=1}^{[n s]} \sum_{j=1}^{[n t]} | Δ_{i,j} Y |^2$ 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.29 pagesProbabilityStatistics Theory62G05, 60F05, 62M40, 60H07text