Convergence of random spectral measures and applications to invariance principles. (Q5933667)

The authors set up a unifying framework for the study of convergence in law for random processes that can be expressed linearly in terms of a weak white noise for which a weak invariance principle holds. They show that the latter is equivalent to the convergence of a sequence of random spectral measures. This allows to weaken the usual hypotheses, which leads to new convergence in law results, especially for long memory processes.