On the characterization of certain point processes

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.