CUMULANTS FOR STATIONARY MIXING RANDOM SEQUENCES AND
APPLICATIONS TO EMPIRICAL SPECTRAL DENSITY
Abstract: We first give a central limit theorem for a stationary strongly mixing sequence
without any mixing rate assumption following ideas of Rosenblatt . We then
study functional central limit convergence and law of the iterated logarithm for the
empirical spectral density considered like a random element of some Sobolev space.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -