Generalized powers of strongly dependent random variables
Files
Published version
Date
1984-11
DOI
Authors
Avram, Florin
Taqqu, Murad S.
Version
OA Version
Citation
F Avram, M Taqqu. 1984. "Generalized Powers of Strongly Dependent Random Variables." Cornell University School of Operations Research and Industrial Engineering Technical Report, Volume 643, http://hdl.handle.net/1813/8527
Abstract
Generalized powers of strongly dependent random variables
Dobrushin, Major and Taqqu have studied the weak convergence of normalized sums of Hm(Yk) where Hm is the Hermite polynomial of order m and where {Yk} is a strongly dependent stationary Gaussian sequence. The limiting process Zm(t) is non-Gaussian when m > l. We study here the weak convergence to Zm(t) of normalized sums of stationary sequences {Uk}. These Uk can be off-diagonal multilinear forms or they can be of the form Uk = pm(\) where the polynomial pm is a generalized power and where \ is a strongly dependent non-Gaussian finite variance moving average.
Dobrushin, Major and Taqqu have studied the weak convergence of normalized sums of Hm(Yk) where Hm is the Hermite polynomial of order m and where {Yk} is a strongly dependent stationary Gaussian sequence. The limiting process Zm(t) is non-Gaussian when m > l. We study here the weak convergence to Zm(t) of normalized sums of stationary sequences {Uk}. These Uk can be off-diagonal multilinear forms or they can be of the form Uk = pm(\) where the polynomial pm is a generalized power and where \ is a strongly dependent non-Gaussian finite variance moving average.