English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A recent result by Barrera and Peligrad shows that the quenched Central LimitTheorem holds for the discrete Fourier transforms (DFT) of a stationary processin $L^2$ if a "random" centering is used. In this note we show that this is anecessary condition by providing an example of a process satisfying thehypothesis of such theorem for which the DFT, without random centering, do notsatisfy a quenched limit theorem. The DFT of this process, by previous resultsby Peligrad and Wu, satisfy the corresponding CLT in the annealed sense.

An Example of non-quenched Convergence in the Conditional CLT for Discrete Fourier Transforms