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Central Limit Theorem for product of dependent random variables

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 نشر من قبل Jun Tao Duan
 تاريخ النشر 2021
  مجال البحث
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Given ${X_k}$ is a martingale difference sequence. And given another ${Y_k}$ which has dependency within the sequence. Assume ${X_k}$ is independent with ${Y_k}$, we study the properties of the sums of product of two sequences $sum_{k=1}^{n} X_k Y_k$. We obtain product-CLT, a modification of classical central limit theorem, which can be useful in the study of random projections. We also obtain the rate of convergence which is similar to the Berry-Essen theorem in the classical CLT.



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