Relative Weak Compactness of Sums of Random Variables
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In this article sufficient conditions for relative weak compactness of sums centered by constants of pair-wise negatively associated randomvariables and for sums of squares of any random variables centered by their medians are given. These conditions become necessary and sufficient if random variables are independent. The conditions are inspired by classical conditions for weak convergence of sums of uniformly small random variables.
KeywordsPair-wise negatively associated random variables relative weak compactness
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- 4.B. V. Gnedenko and A. N. Kolmogorov, Limits Distributions for Sums of Independent Random Variables, 2nd ed. (Addison-Wesley, Cambridge, MA, 1980).Google Scholar