Weak convergence of empirical processes on sequences of stationary random variables (Q801596)

Let \(\{\xi_ n\}\) be a stationary sequence of random variables and \(\{Y_ n\}\) the empirical process defined by \(\{\xi_ n\}\). In this paper, the author showed that a weak convergence theorem for the empirical process \(\{Y_ n\}\) holds if \(\{\xi_ n\}\) is \(\rho\)-mixing with mixing coefficient \(\rho (n)=O(n^{-1/2-\theta})\), and the result improves the reviewer's result in J. Multivariate Anal. 8, 584-588 (1978; Zbl 0402.60023). Further, the author obtained a weak convergence theorem of the empirical process \(\{Y_{N_ n}\}\) with random index when \(\{\xi_ n\}\) is \(\alpha\)-mixing.