Explicit Conditions for the Convergence of Point Processes Associated to Stationary Arrays

2009/12/08 by Raluca Balan, Balan, Raluca, Sana Louhichi +1
Mathematics · #60E07 #60G10 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E07 #msc:60G10

paper · pdf · doi:10.48550/arxiv.0912.1561

arxiv created 2009/12/08 · arxiv updated 2010/01/07

Abstract

In this article, we consider a stationary array (X_j,n)_{1 ≤ j ≤ n, n ≥ 1} of random variables with values in \bR \verb2\2 \0\ (which satisfy some asymptotic dependence conditions), and the corresponding sequence (N_n)_{n≥ 1} of point processes, where N_n has the points X_j,n, 1≤ j ≤ n. Our main result identifies some explicit conditions for the convergence of the sequence (N_n)_{n ≥ 1}, in terms of the probabilistic behavior of the variables in the array.

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