Countable Random Sets: Uniqueness in Law and Constructiveness
Abstract
The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two approaches on uniqueness theorems: First, the study of generators for \sigma-fields used in this context and, secondly, the analysis of hitting functions. The last section of this paper deals with the notion of constructiveness. We will prove a measurable selection theorem and a decomposition theorem for constructive countable random sets, and study constructive countable random sets with independent increments.
Cite
@article{arxiv.1206.6227,
title = {Countable Random Sets: Uniqueness in Law and Constructiveness},
author = {Philip Herriger},
journal= {arXiv preprint arXiv:1206.6227},
year = {2012}
}
Comments
Published in Journal of Theoretical Probability (http://www.springerlink.com/content/0894-9840/). The final publication is available at http://www.springerlink.com