CENTRAL LIMIT-THEOREMS FOR QUADRATIC-FORMS WITH TIME-DOMAIN CONDITIONS

Authors
GIRAITIS L TAQQU MS
Citation
L. Giraitis et Ms. Taqqu, CENTRAL LIMIT-THEOREMS FOR QUADRATIC-FORMS WITH TIME-DOMAIN CONDITIONS, Annals of probability, 26(1), 1998, pp. 377-398
Citations number
23
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
26
Issue
1
Year of publication
1998
Pages
377 - 398
Database
ISI
SICI code
0091-1798(1998)26:1<377:CLFQWT>2.0.ZU;2-N
Abstract
We establish the central limit theorem for quadratic forms Sigma(t, s= 1)(N) b(t-s)P-m,P- n(X-t, X-s) of the bivariate Appell polynomials P-m ,P- n(X-t, X-s) under time-domain conditions. These conditions relate the weights b(t) and the covariances of the sequences (P-m,P- n(X-t, X -s)) and (X-t). The time-domain approach, together with the spectral d omain approach developed earlier, yields a general set of conditions f or central limit theorems.