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Contents of PMS, Vol. 10, Fasc. 1,
pages 11 - 26
 

CUMULANTS FOR STATIONARY MIXING RANDOM SEQUENCES AND APPLICATIONS TO EMPIRICAL SPECTRAL DENSITY

P. Doukhan
J. R. León

Abstract: We first give a central limit theorem for a stationary strongly mixing sequence without any mixing rate assumption following ideas of Rosenblatt [23]. 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: -

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