View More View Less
  • 1 UCV. Departamento de Matemáticas Facultad de Ciencias A.P. Caracas 1041-A Venezuela E-mail
  • 2 Unimet Departamento de Matemáticas Facultad de Ciencias Y Artes Caracas 1070 Venezuela E-mail
Restricted access

Abstract  

Let {X t : 0 ≦ t ≦ 1} be a centered stationary Gaussian process, with correlation function satisfying the condition ρ(t) = 1 − t β L(t), 0 < β < 2, and let L be a slowly varying function at zero. Observing the process at points i/N, i = 0,1,..., N and considering ¦X i/NX (i-1)/N¦p with p > 0, we study the properties of the Donsker line associated with p-th order variations

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sum\limits_{i = 1}^{[N{\text{ }}t]} {|X_{i/N} } - {\text{ }}X_{(i - 1)/N} |^p$$ \end{document}
. We also study the relationship between the number of crossings of a regularization of the initial process and the local time of the initial process. The results depend on the values of β.

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Jun 2020 0 0 0
Jul 2020 0 0 0
Aug 2020 1 0 0
Sep 2020 0 0 0
Oct 2020 0 0 0
Nov 2020 0 1 0
Dec 2020 0 0 0