Complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination spaces

The aim of this study is to establish the complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination space. Our results not only generalize related previously reported results but also improve them. Some illustrative examples are provided.

[1]  Ana Colubi,et al.  A generalized strong law of large numbers , 1999 .

[2]  Yukio Ogura,et al.  Central limit theorems for generalized set-valued random variables , 2003 .

[3]  Nguyen Van Quang,et al.  On the strong laws of large numbers for double arrays of random variables in convex combination spaces , 2012 .

[4]  A. I. Volodin,et al.  On complete convergence for arrays of rowwise independent random elements in banach spaces , 1999 .

[5]  Ilya Molchanov,et al.  The Law of Large Numbers in a Metric Space with a Convex Combination Operation , 2006 .

[6]  Robert L. Taylor Complete convergence for weighted sums of arrays of random elements. , 1983 .

[7]  Nguyen Van Quang,et al.  Strong laws of large numbers for adapted arrays of set-valued and fuzzy-valued random variables in Banach space , 2012, Fuzzy Sets Syst..

[8]  Lynne Seymour,et al.  Weak laws of large numbers for fuzzy random sets , 2001 .

[9]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[10]  Ilya S. Molchanov,et al.  A General Law of Large Numbers, with Applications , 2006, SMPS.

[11]  Li-Xin Zhang,et al.  Strong laws of large numbers for arrays of rowwise independent random compact sets and fuzzy random sets , 2008, Fuzzy Sets Syst..

[12]  Jong-Il Baek,et al.  Retraction Note to: Convergence of Weighted Sums for Arrays of Negatively Dependent Random Variables and Its Applications , 2010 .

[13]  Allan Gut,et al.  Complete convergence for arrays , 1992 .

[14]  Yukio Ogura,et al.  Strong laws of large numbers for independent fuzzy set-valued random variables , 2006, Fuzzy Sets Syst..

[15]  C. Castaing,et al.  Convex analysis and measurable multifunctions , 1977 .

[16]  Ferenc Móricz,et al.  Strong laws of large numbers for arrays of rowwise independent random variables , 1989 .

[17]  H Robbins,et al.  Complete Convergence and the Law of Large Numbers. , 1947, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Volker Krätschmer,et al.  Limit theorems for fuzzy-random variables , 2002, Fuzzy Sets Syst..

[19]  Jong-Il Baek,et al.  RETRACTED: Convergence of weighted sums for arrays of negatively dependent random variables and its applications , 2010 .

[20]  Pedro Terán,et al.  Algebraic, metric and probabilistic properties of convex combinations based on the t-normed extension principle: the strong law of large numbers , 2013, Fuzzy Sets Syst..