The strong law of large numbers for dependent random variables

A general method to the strong law of large numbers and its applications

“…This theorem does not need any restrictions on the dependence structure of random variables and b n is not assumed to satisfy any regularity conditions. As a result of this theorem, Fazekas and Klesov (2001) explored some strong laws of large numbers for martingales and r-mixing sequences, then Kuczmaszewska (2005) proved a strong law of large numbers for negatively associated sequences and extended the result to r-mixing sequences.…”

On a General Approach to the Strong Laws of Large Numbers*

“…Inequality (11) was obtained by Matu la [22] for p = 2. Kuczmaszewska [18] obtained for negatively associated zero mean random variables X 1 , . .…”

“…Using the general Theorem 2, Kuczmaszewska [18] obtained SLLN's for certain dependent random variables. She presented an SLLN for negatively associated sequences.…”

“…Moreover, she proved a general Marcinkiewicz-Zygmund type SLLN for -mixing sequences. Both [8,18] applied the Kolmogorov type maximal inequality for -mixing sequences given in [32]; see (14) above.…”

Permutation Invariant Strong Law of Large Numbers for Exchangeable Sequences

“…sequences of random variables has been generalized into several directions. It has, for example, been generalized for pairwise independent, identically distributed random variables in [1], for nonnegative random variables in [2], for dependent, mixing random variables in [3,4], and for pairwise uncorrelated random variables in [5].…”