An original statistical approach making it possible to accurately model video sequences in the wavelet domain as Gaussian laws is presented. By partitioning the wavelet coefficients into classes with independent elements, we rigorously handle the dependency existing among the successive frames in the video sequence. Further on, four statistical tests are applied to each class in the partition, with the following purposes: (1) to check up the Gaussian law; (2) to validate the data partition and (3) to reveal a homogeneity behaviour among the classes in the partition. Finally, the obtained results are fusioned so as to provide a global information characterising the whole sequence. At the same time, an a posteriori proof concerning an ergodicity behaviour for video sequences is obtained. We integrated these results within a robust video watermarking scheme. The mark is generated according to a CDMA (Code Division Multiple Access) procedure, starting from a 64 bit message (a serial number, a logo, etc). The embedding procedure is a weighted addition of the watermark into the wavelet coefficients featuring the Gaussian behaviour. The detection procedure is based on matched filters, the optimality of which is ensured under the considered framework. The experiments feature firm results concerning all the requirements stated nowadays: obliviousness, transparency, robustness, and probability of false alarm.