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Titlebook: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables; Shoumei Li,Yukio Ogura,Vladik Kreinovich Book 2002 Sp

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书目名称Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables
编辑Shoumei Li,Yukio Ogura,Vladik Kreinovich
视频video
丛书名称Theory and Decision Library B
图书封面Titlebook: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables;  Shoumei Li,Yukio Ogura,Vladik Kreinovich Book 2002 Sp
描述After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975). It is well known that the theory of set-valued random variables is a natural extension of that of general real-valued random variables or random vectors. However, owing to the topological structure of the space of closed sets and special features of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many special properties. This gives new meanings for the classical probability theory. As a result of the development in this area in the past more than 30 years, the theory of set-valued random variables with many applications has become one of new and active branches in probability theory. In practice also, we are often faced with random experiments whose outcomes are not numbers but are expressed in inexact linguistic terms.
出版日期Book 2002
关键词Martingal; Martingale; Random variable; fuzzy; optimization
版次1
doihttps://doi.org/10.1007/978-94-015-9932-0
isbn_softcover978-90-481-6139-3
isbn_ebook978-94-015-9932-0
copyrightSpringer Science+Business Media B.V. 2002
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Convergence Theorems for Fuzzy Set-Valued Random VariablesIn this Chapter we also focus on the case of the basic space . = ℝ., although many results can be obtained in the case in which the basic space is a general Banach space, in particular, for a reflexive Banach space or for .* being separable.
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Applications to ImagingWith this chapter we start describing applications of our set based techniques. Since set theory is the main language of the foundations of mathematics it is natural to expect that set methods can be applied in many application areas — and, as we shall see, symmetry methods related to limit theorems are indeed useful in multiple application areas.
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https://doi.org/10.1007/978-94-015-9932-0Martingal; Martingale; Random variable; fuzzy; optimization
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The Space of Set-Valued Random Variableshroughout this book, assume that (., ║ · ║.)is a Banach space with the dual space .*, 0 denotes the origin of ., . denotes the. one element set {0} and ℝ is the set of all of real numbers. The open unit ball in . is denoted by .. Also we shall adopt particular notation for certain classes of subsets
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Convergence Theorems for Set-Valued Martingalesof the theory of martingales in a Banach space. After this work the theory of the set-valued martingale was studied by several authors such as Neveu [157], Daures [54]. However, owing to the limit of the definition of conditional expectation defined by Van Cutsem the study was restricted to the case
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