Open Access
Translator Disclaimer
December, 1974 Some Functional Limit Theorems for Dependent Random Variables
Alvaro Gonzalez Villalobos
Ann. Probab. 2(6): 1090-1107 (December, 1974). DOI: 10.1214/aop/1176996500

Abstract

We prove theorems on weak convergence of random elements $X_m(\omega, t), 0 \leqq t \leqq 1$, to a Gaussian process. In Part I, these random elements are constructed on the basis of the linear means of a lacunary trigonometric series $\sum a_j \cos n_j\omega$. In Part II, the lacunarity hypothesis is dropped and replaced by the hypothesis of linear independence of the real numbers $n_j$.

Citation

Download Citation

Alvaro Gonzalez Villalobos. "Some Functional Limit Theorems for Dependent Random Variables." Ann. Probab. 2 (6) 1090 - 1107, December, 1974. https://doi.org/10.1214/aop/1176996500

Information

Published: December, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0302.60014
MathSciNet: MR394789
Digital Object Identifier: 10.1214/aop/1176996500

Subjects:
Primary: 60F05
Secondary: 60G15

Keywords: Functional limit theorems for dependent random variables , Gaussian processes , lacunary series , linearly independent numbers

Rights: Copyright © 1974 Institute of Mathematical Statistics

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.2 • No. 6 • December, 1974
Back to Top