Convergence in distribution of point processes on Polish spaces to a simple limit

作者：Peterson Lisa D^*

来源：Statistics & Probability Letters, 2011, 81(12): 1859-1861.

DOI：10.1016/j.spl.2011.07.018

• Convergence in distribution
• Point processes
• Simple point processes
• Polish spaces

Let xi, xi(1), xi(2), ... be a sequence of point processes on a complete and separable metric space (S, d) with xi simple. We assume that P{xi(n)B = 0} -> P{xi B = 0} and lim sup(n ->infinity) P{xi(n)B > 1} <= P{xi B > 1} for all B in some suitable class 2, and show that this assumption determines if the sequence {xi(n)} converges in distribution to xi. This is an extension to general Polish spaces of the weak convergence theory for point processes on locally compact Polish spaces found in Kallenberg (1996).

• 出版日期2011-12