Guyon, Xavier; Leon, José Convergence en loi des H-variations d’un processus gaussien stationnaire sur \({\mathbb{R}}\). (Convergence in law of H-variations of a stationary Gaussian process). (French) Zbl 0691.60017 Ann. Inst. Henri Poincaré, Probab. Stat. 25, No. 3, 265-282 (1989). Let \(\{X,k\geq 1\}\) be a sequence of independent random variables and put \[ S_ n=\sum^{n}_{k=1}X_ k,\quad Z_ n=B_ n^{-1}S_ n-a_ n, \] where \(B_ n>0\) and \(a_ n\) are constants. We assume that \(X_ k\), \(k\geq 1\), has a density function \(f_{X_ k}\). Suppose that \[ \sup_{x}\| F_{Z_ n}(x)-G(x)| \to 0,\quad n\to \infty, \] where G is a distribution function of class L. The main result gives conditions under which \(\sup | f_{Z_ n}(x)-g(x)| \to 0,\) \(n\to \infty,\) where \(g(x)=G'(x).\) Reviewer: D.Szynal Cited in 1 ReviewCited in 38 Documents MSC: 60F05 Central limit and other weak theorems 60G15 Gaussian processes 62M99 Inference from stochastic processes Keywords:convergence in law; H-variations; stationary Gaussian process PDFBibTeX XMLCite \textit{X. Guyon} and \textit{J. Leon}, Ann. Inst. Henri Poincaré, Probab. Stat. 25, No. 3, 265--282 (1989; Zbl 0691.60017) Full Text: Numdam EuDML