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On the characterization of certain point processes

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  • Hsing, Tailen

Abstract

This paper consists of two parts. First, a characterization is obtained for a class of infinitely divisible point processes on . Second, the result is applied to identify the weak limit of the point process Nn with points (j/n, un-1 ([xi]j)), j = 0, ±1, ±2, ..., where {[xi]j} is a stationary sequence satisfying a certain mixed conditio [Delta], and {un} is a sequence of non-increasing functions on (0, [infinity]) such that This application extends a result of Mori [14], which assumes that {[xi]j} is [alpha]-mixing, and that the distribution of max1[less-than-or-equals, slant]j[less-than-or-equals, slant]j [xi]j can be linearly normalized to converge to a maximum stable distribution.

Suggested Citation

  • Hsing, Tailen, 1987. "On the characterization of certain point processes," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 297-316.
    • Handle: RePEc:eee:spapps:v:26:y:1987:i::p:297-316
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    Cited by:

    1. Novak, S. Y., 2002. "Multilevel clustering of extremes," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 59-75, January.
    2. Tyran-Kaminska, Marta, 2010. "Convergence to Lévy stable processes under some weak dependence conditions," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1629-1650, August.

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