A unified approach to central limit theorems for weakly associated stationary sequences

Adam Jakubowski

Stochastic Processes and their Applications, 2026, vol. 196, issue C

Abstract: For a weakly associated and stationary sequence we give conditions which guarantee that partial sums of this sequence, under natural normalization, converge in distribution to a Gaussian limit. Our approach unifies both the standard CLT due to Newman and the CLT for sums of i.i.d. random variables with infinite variance. It is also homogeneous in the sense that it refers to truncated covariances only. As usually, the obtained limit theorem admits a natural extension to the functional convergence. The case of weakly associated and stationary random vectors is also considered.

Keywords: Association; Weak association; Slow variation; Central limit theorem; Functional convergence; Infinite variance (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2026.104916

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