Avram, FlorinTaqqu, Murad S.2018-09-052018-09-051984-11F 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/1813/8527https://hdl.handle.net/2144/31167Generalized powers of strongly dependent random variablesDobrushin, 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.Appell polynomialsSelf-similar processesMultiple Wiener-Ito integralsLong-range dependenceWeak convergenceOperations researchIndustrial engineeringTechnical reportTechnical Report0000-0002-1145-9082 (Taqqu, M)