Competing particle systems and the Ghirlanda-Guerra identities.
Let be a doubly infinite sequence of identically distributed -mixing random variables, and an absolutely summable sequence of real numbers. We prove the complete -order moment convergence for the partial sums of moving average processes based on the sequence of -mixing random variables under some suitable conditions. These results generalize and complement earlier results.
The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the -measure of non-exchangeability for copulas belonging to this class.
We present conditions sufficient for the weak convergence to a compound Poisson distribution of the distributions of the kth order statistics for extremes of moving minima in arrays of independent random variables.
In this paper, we apply the technique of decoupling to obtain some exponential inequalities for semi-bounded martingale, which extend the results of de la Peña, Ann. probab. 27 (1999) 537–564.