It is proved that the spectral densities of arrays of weakly stationary processes fulfilling a certain regularity condition converge uniformly to a continuous spectral density.
@article{1176993242,
author = {Falk, M.},
title = {On the Convergence of Spectral Densities of Arrays of Weakly Stationary Processes},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 918-921},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993242}
}
Falk, M. On the Convergence of Spectral Densities of Arrays of Weakly Stationary Processes. Ann. Probab., Tome 12 (1984) no. 4, pp. 918-921. http://gdmltest.u-ga.fr/item/1176993242/