Accession Number:

ADA179267

Title:

On the Existence and Convergence of Probability Measures on Continuous Semi-Lattices.

Descriptive Note:

Technical rept.,

Corporate Author:

NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES

Personal Author(s):

Report Date:

1986-08-01

Pagination or Media Count:

62.0

Abstract:

This paper studies probability measures on continuous lattices and, more generally, continuous semi-lattices. It characterizes probability measures by distribution functions, it characterizes weak convergence of probability measures by pointwise convergence of distribution functions and it provides a Levy-Khinchin representation of all infinitely divisible distributions. By applying the general results to special cases this paper extends some well-known results for random closed sets in locally compact second countable Hausdorff spaces to non-Hausdorff spaces. It also provides some new results for random compact sets and random compact convex sets in Euclidean spaces.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE