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

Raluca Balan; Sana Louhichi

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arXiv · 0912.1561

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

Raluca Balan·Sana Louhichi

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Abstract

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

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Raluca Balan, Sana Louhichi. 2009-12-08. Explicit Conditions for the Convergence of Point Processes Associated to Stationary Arrays. https://arxiv.org/abs/0912.1561

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