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

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  • Jakubowski, Adam

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.

Suggested Citation

  • Jakubowski, Adam, 2026. "A unified approach to central limit theorems for weakly associated stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:spapps:v:196:y:2026:i:c:s0304414926000487
    DOI: 10.1016/j.spa.2026.104916
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    References listed on IDEAS

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    1. Jakubowski, Adam, 1993. "Minimal conditions in p-stable limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 44(2), pages 291-327, February.
    2. Paulo Eduardo Oliveira, 2012. "Asymptotics for Associated Random Variables," Springer Books, Springer, number 978-3-642-25532-8, January.
    3. Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
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