On the characterization of certain point processes

Tailen Hsing

Stochastic Processes and their Applications, 1987, vol. 26, 297-316

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.

Keywords: extreme; values; infinite; divisibility; point; processes; weak; convergence (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (2)

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