Exponential inequalities for dependent random variables (Q1178651)

Exponential inequalities of the Kolmogorov type (upper and lower bounds) are presented for \(\phi\)-mixing, \(\rho\)-mixing and \(\alpha\)-mixing r.v.s. The proofs use martingale techniques, in particular two inequalities due to \textit{W. F. Stout} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 15, 279--290 (1970; Zbl 0209.49004)]. The inequalities given are interesting but the application presented, a law of the iterated logarithm for \(\alpha\)- mixing sequences, is covered by a theorem of \textit{H. Oodaira} and \textit{K. Yoshihara} [Kōdai Math. Sem. Rep. 23, 311--334 (1971; Zbl 0234.60034), \S\ 3, Theorem 5].