Doukhan, P.; León, J. R. Cumulants for stationary mixing random sequences and applications to empirical spectral density. (English) Zbl 0684.60027 Probab. Math. Stat. 10, No. 1, 11-26 (1989). A central limit theorem is derived for a strongly mixing stationary sequence under finiteness of cumulant sums and without any mixing rate assumption. Then a law of iterated logarithm is obtained. Further, the authors study the behaviour of empirical spectral density and present some applications of general results. Reviewer: J.Andel Cited in 10 Documents MSC: 60G10 Stationary stochastic processes 60F05 Central limit and other weak theorems Keywords:central limit theorem; strongly mixing stationary sequence; mixing rate; law of iterated logarithm; empirical spectral density PDFBibTeX XMLCite \textit{P. Doukhan} and \textit{J. R. León}, Probab. Math. Stat. 10, No. 1, 11--26 (1989; Zbl 0684.60027)