Электронная книга: Troffaes Matthias C.M. «Lower Previsions»

 This book has two main purposes. On the one hand, it provides a concise and systematic development of the theory of lower previsions, based on the concept of acceptability, in spirit of the work of Williams and Walley. On the other hand, it also extends this theory to deal with unbounded quantities, which abound in practical applications. Following Williams, we start out with sets of acceptable gambles. From those, we derive rationality criteria–avoiding sure loss and coherence–and inference methods–natural extension–for (unconditional) lower previsions. We then proceed to study various aspects of the resulting theory, including the concept of expectation (linear previsions), limits, vacuous models, classical propositional logic, lower oscillations, and monotone convergence. We discuss n-monotonicity for lower previsions, and relate lower previsions with Choquet integration, belief functions, random sets, possibility measures, various integrals, symmetry, and representation theorems based on the Bishop-De Leeuw theorem. Next,we extend the framework of sets of acceptable gambles to consider also unbounded quantities. As before, we again derive rationality criteria and inference methods for lower previsions, this time also allowing for conditioning. We apply this theory to construct extensions of lower previsions from bounded random quantities to a larger set of random quantities, based on ideas borrowed from the theory of Dunford integration. A first step is to extend a lower prevision to random quantities that are bounded on the complement of a null set (essentially bounded random quantities). This extension is achieved by a natural extension procedure that can be motivated by a rationality axiom stating that adding null random quantities does not affect acceptability. In a further step, we approximate unbounded random quantities by a sequences of bounded ones, and, in essence, we identify those for which the induced lower prevision limit does not depend on the details of the approximation. We call those random quantities'previsible'. We study previsibility by cut sequences, and arrive at a simple sufficient condition. For the 2-monotone case, we establish a Choquet integral representation for the extension. For the general case, we prove that the extension can always be written as an envelope of Dunford integrals. We end with some examples of the theory. Издательство: "John Wiley&Sons Limited" ISBN: 9781118762646 электронная книга Купить за 8507.17 руб и скачать на Litres

Другие книги схожей тематики:

АвторКнигаОписаниеГодЦенаТип книги
Thomas AugustinIntroduction to Imprecise ProbabilitiesIn recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience… — John Wiley&Sons Limited, Подробнее...
9188.33электронная книга

Look at other dictionaries:

• Imprecise probability — The notion of Imprecise probability is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference… …   Wikipedia

• SIPTA — The Society for Imprecise Probability: Theories and Applications (SIPTA) was created in February 2002, with the aim of promoting the research on Imprecise probability. This is done through a series of activities for bringing together researchers… …   Wikipedia

• Provence — For other uses, see Provence (disambiguation). Not to be confused with Province. Location of the former French province of Provence …   Wikipedia

• Controverses sur le réchauffement climatique — Les controverses sur le réchauffement climatique portent sur les points suivants : l existence du réchauffement climatique : au sein de la communauté scientifique, l existence n est plus mise en doute, mais l ampleur du réchauffement l… …   Wikipédia en Français

• Krach immobilier américain des années 2000 — Le krach immobilier américain des années 2000 correspond à la phase de correction du marché liée à l explosion de la bulle immobilière américaine des années 2000. Celui ci fait suite au sommet de l indice national des prix immobiliers observé en… …   Wikipédia en Français

• Jun'ichirō Koizumi — Mandats 56e Premier ministre du Japon 26  …   Wikipédia en Français

• CinemaScore — Cet article concerne une société de sondage pour le cinéma, ne pas confondre avec CinemaScope. CinemaScore est une société de recherche de marché implantée à Las Vegas dans le Nevada. Cette société étudie la fréquentation d un film afin d évaluer …   Wikipédia en Français

• Pomme de terre transgénique — Pommes de terre transgénique Amflora Une pomme de terre transgénique est une variété de pomme de terre (Solanum tuberosum) dérivée d une variété existante génétiquement modifiée par transgenèse, c est à dire dont le …   Wikipédia en Français

• Naoto Kan — 菅 直人 Naoto Kan en 2010 Mandats 61e Premier ministre du Japon …   Wikipédia en Français

• Paris — This article is about the capital of France. For other uses, see Paris (disambiguation). Paris Motto: Fluctuat nec mergitur (Latin: It is tossed by the waves, but does not sink ) …   Wikipedia