Foundations of Constructive Probability Theory
Foundations of Constructive Probability Theory

Author: Yuen-Kwok Chan

Publisher: Cambridge University Press

Published: 2021-05-27

Total Pages: 627

ISBN-13: 1108875572

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Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.

Foundations of Modern Probability
Foundations of Modern Probability

Author: Olav Kallenberg

Publisher: Springer Science & Business Media

Published: 2002-01-08

Total Pages: 670

ISBN-13: 9780387953137

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The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Foundations of Probability
Foundations of Probability

Author: Alfréd Rényi

Publisher: Courier Dover Publications

Published: 2007

Total Pages: 396

ISBN-13:

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Introducing many innovations in content and methods, this book involves the foundations, basic concepts, and fundamental results of probability theory. Geared toward readers seeking a firm basis for study of mathematical statistics or information theory, it also covers the mathematical notions of experiments and independence. 1970 edition.

Theories of Probability
Theories of Probability

Author: Terrence L. Fine

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 276

ISBN-13: 1483263894

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Theories of Probability: An Examination of Foundations reviews the theoretical foundations of probability, with emphasis on concepts that are important for the modeling of random phenomena and the design of information processing systems. Topics covered range from axiomatic comparative and quantitative probability to the role of relative frequency in the measurement of probability. Computational complexity and random sequences are also discussed. Comprised of nine chapters, this book begins with an introduction to different types of probability theories, followed by a detailed account of axiomatic formalizations of comparative and quantitative probability and the relations between them. Subsequent chapters focus on the Kolmogorov formalization of quantitative probability; the common interpretation of probability as a limit of the relative frequency of the number of occurrences of an event in repeated, unlinked trials of a random experiment; an improved theory for repeated random experiments; and the classical theory of probability. The book also examines the origin of subjective probability as a by-product of the development of individual judgments into decisions. Finally, it suggests that none of the known theories of probability covers the whole domain of engineering and scientific practice. This monograph will appeal to students and practitioners in the fields of mathematics and statistics as well as engineering and the physical and social sciences.

Foundations of the Theory of Probability (Classic Reprint)
Foundations of the Theory of Probability (Classic Reprint)

Author: A. N. KOLMOGOROV

Publisher: Forgotten Books

Published: 2017-11-20

Total Pages: 0

ISBN-13: 9780331497120

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Excerpt from Foundations of the Theory of Probability The purpose of this monograph is to give an axiomatic foundation for the theory of probability. The author set himself the task of putting in the1r natural place, among the general notions of modern mathematics, the basic concepts of probability theory - concepts which until recently were considered to be quite peculiar. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.