The central limit theorem for cross-variation related to the standard Brownian sheet and Berry-Esseen bounds

By applying the techniques of Malliavin calculus, we study a central limit theorem of cross-variation related to the standard Brownian sheet. Moreover, we provide the exact Berry-Esseen bound on the Kolmogorov distance by using a recent result proven by Nourdin and Peccati [Nourdin, I., & Peccati, G. (2009b). Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields. Annals of Probability, 37(6), 2231-2261].