Convergence of Probability Measures

TL;DR: The comparison theorem on moment inequalities between negatively associated and independent random variables extends the Hoeffding inequality on the probability bounds for the sum of a random sample without replacement from a finite population as discussed by the authors.

TL;DR: In this article, a method for proving weak convergence in a function-space setting when regular variation is a sufficient condition is presented, where point processes and weak convergence techniques involving continuity arguments play a central role.

TL;DR: In this paper, the weak laws of large numbers for uniformly integrable L1-mixingales are provided. But the L1mixingale condition is weaker than most conditions considered in the literature.

TL;DR: In this article, the authors considered the maxima of independent Weiner processes spatially normalized with time scales compressed and showed that a weak limit process exists, and their one-dimensional distributions are of standard extreme-value type.