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arXiv · 2305.13001

Strong approximations for a class of dependent random variables with semi exponential tails

C Cuny·J Dedecker·F Merlevède
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Abstract

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 subexponential 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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C Cuny, J Dedecker, F Merlevède. 2023-05-22. Strong approximations for a class of dependent random variables with semi exponential tails. https://arxiv.org/abs/2305.13001

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