一类具有半指数尾的相关随机变量的强逼近

Pub Date : 2023-12-06 DOI:10.1007/s10959-023-01306-0

Christophe Cuny, Jérôme Dedecker, Florence Merlevède

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引用次数: 0

摘要

对于耦合系数以次指数速率递减的半指数尾相依随机变量和，我们给出了其几乎确定不变原理下的收敛速率。我们证明了在强不变性原理中的速率是\(\log n\)的幂。我们将我们的结果应用于随机矩阵的id乘积。

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Strong Approximations for a Class of Dependent Random Variables with Semi-Exponential Tails

We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi-exponential tails, whose coupling coefficients decrease at a sub-exponential rate. We show that the rates in the strong invariance principle are in powers of \(\log n\). We apply our results to iid products of random matrices.

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