Explicit Conditions for the Convergence of Point Processes Associated to Stationary Arrays
Abstract
In this article, we consider a stationary array (Xj,n)1 ≤ j ≤ n, n ≥ 1 of random variables with values in 2\2 \0\ (which satisfy some asymptotic dependence conditions), and the corresponding sequence (Nn)n≥ 1 of point processes, where Nn has the points Xj,n, 1≤ j ≤ n. Our main result identifies some explicit conditions for the convergence of the sequence (Nn)n ≥ 1, in terms of the probabilistic behavior of the variables in the array.
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