An analogue of Kolmogorov's law of the iterated logarithm for arrays

An Analogue of the Law of the Iterated Logarithm

On the law of the iterated logarithm.

The law of the iterated logarithm provides a family of bounds all of the same order such that with probability one only finitely many partial sums of a sequence of independent and identically distributed random variables exceed some members of the family, while for others infinitely many do so. In the former case, the total number of such excesses has therefore a proper probability distribution...

The law of the iterated logarithm for LNQD sequences

Let [Formula: see text] be a stationary LNQD sequence of random variables with zero means and finite variance. In this paper, by the Kolmogorov type maximal inequality and Stein's method, we establish the result of the law of the iterated logarithm for LNQD sequence with less restriction of moment conditions. We also prove the law of the iterated logarithm for a linear process generated by an L...

The Law of the Iterated Logarithm for p-Random Sequences

The stochastic properties of p-random sequences are studied in this paper. It is shown that the law of the iterated logarithm holds for p-random sequences. This law gives a quantitative characterization of the density of p-random sets. When combined with the invari-ance property of p-random sequences, this law is also useful in proving that some complexity classes have p-measure 0.

The law of the iterated logarithm for character ratios

Recently, Fulman developed some general connections between martingales and character ratios of a random representation of the symmetric group on transitions, and obtained a convergence rate in a central limit theorem. In this work we aim to establish the law of the iterated logarithm for character ratios. The technique is a well-known Skorokhod embedding theorem for martingales and strong appr...