On random almost periodic trigonometric polynomials and applications to ergodic theory

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dc.creatorCohen, Guy
dc.creatorCuny, Christophe
dc.date2006-02-24
dc.date.accessioned2026-07-07T07:03:44Z
dc.date.available2026-07-07T07:03:44Z
dc.descriptionWe study random exponential sums of the form $\sum_{k=1}^nX_k\times\ex p\{i(λ_k^{(1)}t_1+...+λ_k^{(s)}t_s)\}$, where $\{X_n\}$ is a sequence of random variables and $\{λ_n^{(i)}:1\leq i\leq s\}$ are sequences of real numbers. We obtain uniform estimates (on compact sets) of such sums, for independent centered $\{X_n\}$ or bounded $\{X_n\}$ satisfying some mixing conditions. These results generalize recent results of Weber [Math. Inequal. Appl. 3 (2000) 443--457] and Fan and Schneider [Ann. Inst. H. Poincaré Probab. Statist. 39 (2003) 193--216] in several directions. As applications we derive conditions for uniform convergence of these sums on compact sets. We also obtain random ergodic theorems for finitely many commuting measure-preserving point transformations of a probability space. Finally, we show how some of our results allow to derive the Wiener--Wintner property (introduced by Assani [Ergodic Theory Dynam. Systems 23 (2003) 1637--1654]) for certain functions on certain dynamical systems.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117905000000459 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0602543
dc.identifierhttp://arxiv.org/abs/math/0602543
dc.identifierAnnals of Probability 2006, Vol. 34, No. 1, 39-79
dc.identifierdoi:10.1214/009117905000000459
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109091
dc.subjectProbability
dc.subject37A50, 60F15 (Primary) 47A35, 42A05 (Secondary)
dc.titleOn random almost periodic trigonometric polynomials and applications to ergodic theory
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