Further Spitzer\u2019s law for widely orthant dependent random variables

Pingyan Chen,Soo Hak Sung,Jingjing Luo

doi:10.1186/s13660-021-02718-4

Pingyan Chen, Soo Hak Sung + Show 1 more

Open Access

https://doi.org/10.1186/s13660-021-02718-4

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Abstract

The Spitzer’s law is obtained for the maximum partial sums of widely orthant dependent random variables under more optimal moment conditions.

Highlights

Introduction and main resultsIt is well known that the sample mean, based on a sequence of independent random variables with common distribution, is a strongly consistent estimator for the population mean
Using Etemadi’s subsequence method, Kruglov [8] gave a sufficient condition for the Kolmogorov strong law of large numbers for nonnegative random variables as follows
We provide a more optimal moment condition when g is a fairly general function containing above functions

Summary

Introduction

Introduction and main resultsIt is well known that the sample mean, based on a sequence of independent random variables with common distribution, is a strongly consistent estimator for the population mean. Chen and Sung [3] obtained Spitzer’s law for maximum partial sums of WOD random variables as follows. We improve the moment condition when g(x) = max{1, xα}, logα x, (log log x)α for some α > 0.

Results

Conclusion