Countable Random Sets: Uniqueness in Law and Constructiveness

Philip Herriger ()
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Philip Herriger: Eberhard Karls Universität Tübingen

Journal of Theoretical Probability, 2013, vol. 26, issue 3, 781-802

Abstract: Abstract The first part of this article deals with theorems on uniqueness in law for σ-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 σ-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 prove a measurable selection theorem and a decomposition theorem for constructive countable random sets, and study constructive countable random sets with independent increments.

Keywords: Constructive countability; Constructiveness; Countable random sets; Decomposition; Generators; Hitting functions; Independent increments; Measurable selections; Point processes; Poisson processes; Rényi; Uniqueness in law; 60G55; 60D05; 28B20 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-012-0432-5

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