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

2023/05/22 by Cuny, C, Dedecker, J, Merlevède, F
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2305.13001

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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