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• W2117457918 abstract "For each n≥1, let {X j,n }1≤j≤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 $N_{n}=sum_{j=1}^{n}delta_{X_{j,n}}$ to an infinitely divisible point process. From the point process convergence we obtain the convergence in distribution of the partial sum sequence S n =∑ =1 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." @default.
• W2117457918 created "2016-06-24" @default.
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• W2117457918 date "2008-06-13" @default.
• W2117457918 modified "2023-10-03" @default.
• W2117457918 title "Convergence of Point Processes with Weakly Dependent Points" @default.
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• W2117457918 doi "https://doi.org/10.1007/s10959-008-0176-4" @default.
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