The Other 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...

An Analogue of the Law of the Iterated Logarithm

On the other law of the iterated logarithm for self-normalized sums.

In this note, we obtain a Chung's integral test for self-normalized sums of i.i.d. random variables. Furthermore, we obtain a convergence rate of Chung law of the iterated logarithm for self-normalized sums.

The Law of the Iterated Logarithm in Analaysis

In this paper, we first discuss the history of the law of the iterated logarithm. We then focus our discussion on how it was introduced in analysis. Finally we mention different types of law of the iterated logarithm and state some of the recent developments. In order to discuss the history and developments of law of the iterated logarithm, some definitions and theorems are in order: Definition...

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...