21 research outputs found
Countable Random Sets: Uniqueness in Law and Constructiveness
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.Comment: Published in Journal of Theoretical Probability
(http://www.springerlink.com/content/0894-9840/). The final publication is
available at http://www.springerlink.co
Consonant Random Sets: Structure and Properties
Abstract. In this paper, we investigate consonant random sets from the point of view of lattice theory. We introduce a new definition of consonancy and study its relationship with possibility measures as upper probabilities. This allows us to improve a number of results from the literature. Finally, we study the suitability of consonant random sets as models of the imprecise observation of random variables
Existence of solutions for generalized differential equations with unbounded right-hand side
Random Measurable SelectionsHorizons of the Mind. A Tribute to Prakash Panangaden
We make the first steps towards showing a general \u201crandomness for free\u201d theorem for stochastic automata. The goal of such theorems is to replace randomized schedulers by averages of pure schedulers. Here, we explore the case of measurable multifunctions and their measurable selections. This involves constructing probability measures on the measurable space of measurable selections of a given measurable multifunction, which seems to be a fairly novel problem. We then extend this to the case of IT automata, namely, non-deterministic (infinite) automata with a history-dependent transition relation. Throughout, we strive to make our assumptions minimal