Displaying similar documents to “An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law”

An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law

Hartmut Lanzinger (2010)

ESAIM: Probability and Statistics

Similarity:

We prove a strong law of large numbers for moving averages of independent, identically distributed random variables with certain subexponential distributions. These random variables show a behavior that can be considered intermediate between the classical strong law and the Erdös-Rényi law. We further show that the difference from the classical behavior is due to the influence of extreme terms.

Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays

Zakhar Kabluchko, Axel Munk (2009)

ESAIM: Probability and Statistics

Similarity:

We generalize a theorem of Shao [ (1995) 575–582] on the almost-sure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation result in the multidimensional setting. The multiscale statistic under consideration was used recently for the selection of the regularization parameter in a number of statistical algorithms as well...

A note on the almost sure limiting behavior of the maximun of a sequence of partial sums.

André Adler (1988)

Stochastica

Similarity:

The goal of this paper is to show that, in most strong laws of large numbers, the n partial sum can be replaced with the largest of the first n sums. Moreover it is shown that the usual assumptions of independence and common distribution are unnecessary and that these results apply also to strong laws for Banach valued random elements.

Exact laws for sums of ratios of order statistics from the Pareto distribution

André Adler (2006)

Open Mathematics

Similarity:

Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).

One sided strong laws for random variables with infinite mean

André Adler (2017)

Open Mathematics

Similarity:

This paper establishes conditions that secure the almost sure upper and lower bounds for a particular normalized weighted sum of independent nonnegative random variables. These random variables do not possess a finite first moment so these results are not typical. These mild conditions allow us to show that the almost sure upper limit is infinity while the almost sure lower bound is one.