Strong Laws of Large Numbers for Double Arrays of Independent Set-Valued Random Variables in Banach Spaces

Van Quang Nguyen; Tran Thuan Nguyen

Abstract

We establish some strong laws of large numbers for double arrays of independent set-valued random variables in separable Banach spaces under various conditions.

Author information

Contact details are reproduced from the original publication and may be historical.

Van Quang Nguyen

Dept. of Mathematics, Vinh University, Nghe An Province, Viet Nam

nvquang@hotmail.com

Tran Thuan Nguyen

Dept. of Mathematics, Vinh University, Nghe An Province, Viet Nam

tranthuandhv@gmail.com

Keywords

Double array
triangular array
strong law of large numbers
independent
compactly uniformly integrable
stochastically dominated
uniformly p-smooth
martingale

Mathematics Subject Classification

28B20, 60G42, 46A17, 54A20

Suggested citation

V. Q. Nguyen, T. T. Nguyen. “Strong Laws of Large Numbers for Double Arrays of Independent Set-Valued Random Variables in Banach Spaces.” Journal of Convex Analysis 19 (2012), No. 1, 141–157.