Abstract
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.
Citation
Christian Houdre. "On the Almost Sure Convergence of Series of Stationary and Related Nonstationary Variables." Ann. Probab. 23 (3) 1204 - 1218, July, 1995. https://doi.org/10.1214/aop/1176988180
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