Convergence of Point Processes with Weakly Dependent Points

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dc.creatorBalan, Raluca
dc.creatorLouhichi, Sana
dc.date2008-05-27
dc.date.accessioned2026-07-07T09:41:07Z
dc.date.available2026-07-07T09:41:07Z
dc.descriptionFor each $n \geq 1$, let $\{X_{j,n}\}_{1 \leq j \leq n}$ be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions for the convergence in distribution of the point process $N_n=\sum_{j=1}^{n}δ_{X_{j,n}}$ to an infinitely divisible point process. From the point process convergence, we obtain the convergence in distribution of the partial sum sequence $S_n=\sum_{j=1}^{n}X_{j,n}$ to an infinitely divisible random variable, whose Lévy measure is related to the canonical measure of the limiting point process. As examples, we discuss the case of triangular arrays which possess known (row-wise) dependence structures, like the strong mixing property, the association, or the dependence structure of a stochastic volatility model.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/0805.4128
dc.identifierhttp://arxiv.org/abs/0805.4128
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161715
dc.subjectProbability
dc.subject60F05; 60E07
dc.titleConvergence of Point Processes with Weakly Dependent Points
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