Strong law of large numbers for negatively associated
Abstract:
Associated random variables inherit some properties of independent random variables. This fact allows to suggest that the main probability laws which are true for sums of independent random variables have their analo-
giesfor negative associated random variables. Obviously this analogy cannot be direct. For example, the Central Limit Theorem may not hold for negative associated random variables with _nitevariance. In the talk we discuss that the law of large numbers in strong form is satis_edfor negatively associated random variables as soon as it is applicable for independent random variables with identical marginal distributions, or, more precise, if the classical assumptions of law of large numbers are ful_lled. This means that the classical assumptions are necessary and su_cientfor the validity of the law of large numbers for negatively associated random variables. Hence, the main goal of this study is to investigate the assumptions of the validity for the strong law of large numbers for negatively associated random variables. It is established that many criterions for the strong law of large numbers for independent random variables are applicable for negatively associated random variables. The results are of theoretical nature and the main importance of the work is in the extension of laws of large numbers 1
from independent case to negatively associated random variables. We provide generalizations of classical strong law of large numbers for the case of negatively associated random variables. We followed ideas of Kolmogorov
Tea Time:2:40pm, R707 (七樓休息室)