On Strong Convergence for Weighted Sums of a Class of Random Variables

Abstract

Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mo stretchy="false">{</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">}</mml:mo></mml:mrow></mml:math>be a sequence of random variables satisfying the Rosenthal-type maximal inequality. Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition. As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained. Our result generalizes the corresponding one of Zhou et al. (2011) and improves the corresponding one of Wang et al. (2011, 2012).

Locations

• Project Euclid (Cornell University) - View - PDF
• DOAJ (DOAJ: Directory of Open Access Journals) - View
• Abstract and Applied Analysis - View - PDF