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Convergence rates in the strong law for associated random variables

Louhichi S.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 1

203--214

We prove the Marcinkiewicz-Zygmund SLLN (MZ-SLLN) of order p,p ∈[1,2[, for associated sequences, not necessarily stationary. Our assumption on the moment of the random variables is minimal. We present an example of an associated and strongly mixing sequence, with infinite variance, to which our results apply. The conditions yielding such results for this example are discussed.

On the almost sure central limit theorem for associated random variables

Matula P.

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 2

411--416

The aim of this note is to prove the strong version of the CLT for associated sequences without any strong approximation theorems. In the proofs we only apply the weighted convergence result for averages of associated random variables and the standard CLT.