Central limit theorems for quadratic forms with time-domain conditions
Giraitis, Liudas ; Taqqu, Murad S.
Ann. Probab., Tome 26 (1998) no. 1, p. 377-398 / Harvested from Project Euclid
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We establish the central limit theorem for quadratic forms $\Sigma_{t, s=1}^N b(t - s)P_{m, n} (X_t, X_s)$ of the bivariate Appell polynomials $P_{m, n} (X_t, X_x))$ under time-domain conditions. These conditions relate the weights $b(t)$ and the covariances of the sequences $(P_{m, n} (X_t, X_s))$ and $(X_t)$. The time-domain approach, together with the spectral domain approach developed earlier, yields a general set of conditions for central limit theorems.
Publié le : 1998-01-14
Classification:  Appell polynomials,  central limit theorem,  long-range dependence,  quadratic forms,  time series,  60F05,  62M10 
@article{1022855425,
     author = {Giraitis, Liudas and Taqqu, Murad S.},
     title = {Central limit theorems for quadratic forms with time-domain
 conditions},
     journal = {Ann. Probab.},
     volume = {26},
     number = {1},
     year = {1998},
     pages = { 377-398},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1022855425}
}

Giraitis, Liudas; Taqqu, Murad S. Central limit theorems for quadratic forms with time-domain
 conditions. Ann. Probab., Tome 26 (1998) no. 1, pp.  377-398. http://gdmltest.u-ga.fr/item/1022855425/