Описание: This book presents a clear, systematic treatment of convergence theorems of set-valued random variables (random sets) and fuzzy set-valued random variables (random fuzzy sets). Topics such as strong laws of large numbers and central limit theorems, including new results in connection with the theory of empirical processes are covered. The author's own recent developments on martingale convergence theorems and their applications to data processing are also included. The mathematical foundations along with a clear explanation such as HГ¶lmander's embedding theorem, notions of various convergence of sets and fuzzy sets, Aumann integrals, conditional expectations, selection theorems, measurability and integrability arguments for both set-valued and fuzzy set-valued random variables and newly obtained optimizations techniques based on invariant properties are also given.
Описание: This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from
information theory. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit
Автор: Hans Fischer Название: A History of the Central Limit Theorem ISBN: 1461427010 ISBN-13(EAN): 9781461427018 Издательство: Springer Рейтинг: Цена: 17241 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. Coverage extends to the historical development of analytical probability theory and its tools.
Автор: Fischer Название: A History of the Central Limit Theorem ISBN: 0387878564 ISBN-13(EAN): 9780387878560 Издательство: Springer Рейтинг: Цена: 15674 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Автор: Swinburne, Richard Название: Bayes`s Theorem ISBN: 0197263410 ISBN-13(EAN): 9780197263419 Издательство: Oxford Academ Рейтинг: Цена: 2301 р. Наличие на складе: Поставка под заказ.
Описание: Bayes's theorem is a tool for assessing how probable evidence makes some hypothesis. The papers in this volume consider the worth and applicability of the theorem. Richard Swinburne sets out the philosophical issues. Elliott Sober argues that there are other criteria for assessing hypotheses. Colin Howson, Philip Dawid and John Earman consider how the theorem can be used in statistical science, in weighing evidence in criminal trials, and in assessing evidence for the occurrence of miracles. David Miller argues for the worth of the probability calculus as a tool for measuring propensities in nature rather than the strength of evidence. The volume ends with the original paper containing the theorem, presented to the Royal Society in 1763.
Описание: Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-dimensional vector space started in 1969. Currently, this theory is still in progress and promises interesting applications. Parallel to this, similar stability concepts for probabilities on groups were developed during recent decades. It turns out that the existence of suitable limit distributions has a strong impact on the structure of both the normalizing automorphisms and the underlying group. Indeed, investigations in limit laws led to contractable groups and - at least within the class of connected groups - to homogeneous groups, in particular to groups that are topologically isomorphic to a vector space. Moreover, it has been shown that (semi)-stable measures on groups have a vector space counterpart and vice versa. The purpose of this book is to describe the structure of limit laws and the limit behaviour of normalized i.i.d. random variables on groups and on finite-dimensional vector spaces from a common point of view. This will also shed a new light on the classical situation. Chapter 1 provides an introduction to stability problems on vector spaces. Chapter II is concerned with parallel investigations for homogeneous groups and in Chapter III the situation beyond homogeneous Lie groups is treated. Throughout, emphasis is laid on the description of features common to the group- and vector space situation. Chapter I can be understood by graduate students with some background knowledge in infinite divisibility. Readers of Chapters II and III are assumed to be familiar with basic techniques from probability theory on locally compact groups.
ООО "Логосфера " Тел:+7(495) 980-12-10 www.logobook.ru