On the Almost Sure Convergence of Series of Stationary and Related Nonstationary Variables

Houdre, Christian

Ann. Probab., Tome 23 (1995) no. 3, p. 1204-1218 / Harvested from Project Euclid

Résumé

Let $\{X_n\}$ be, for example, a weakly stationary sequence or a lacunary system with finite $p$th moment, $1 \leq p \leq 2$, and let $\{a_n\}$ be a sequence of scalars. We obtain here conditions which ensure the almost sure convergence of the series $\sum a_nX_n$. When $\{X_n\}$ is an orthonormal sequence, the classical Rademacher-Menchov theorem is recovered. This is then applied to study the strong consistency of least squares estimates in multiple regression models.

Publié le : 1995-07-14
Classification: Stationary sequences, series, almost sure convergence, Rademacher-Menchov theorem, $S \alpha S$ harmonizable sequences, strong consistency, least squares, multiple regression, $S_p$-systems, stationary Markov chains, weak dependence, mixing, 60F15, 60G10, 60G12, 60E07

@article{1176988180,
     author = {Houdre, Christian},
     title = {On the Almost Sure Convergence of Series of Stationary and Related Nonstationary Variables},
     journal = {Ann. Probab.},
     volume = {23},
     number = {3},
     year = {1995},
     pages = { 1204-1218},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988180}
}

Houdre, Christian. On the Almost Sure Convergence of Series of Stationary and Related Nonstationary Variables. Ann. Probab., Tome 23 (1995) no. 3, pp.  1204-1218. http://gdmltest.u-ga.fr/item/1176988180/