Foundations of the Theory of Probability

Second English Edition

Author: A.N. Kolmogorov

Publisher: Courier Dover Publications

ISBN: 0486829790

Category: Mathematics

Page: 96

View: 3061

This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.
Posted in Mathematics

Grundbegriffe der Wahrscheinlichkeitsrechnung

Author: A. Kolomogoroff

Publisher: Springer-Verlag

ISBN: 3642498884

Category: Mathematics

Page: 62

View: 2528

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Posted in Mathematics

Theories of Probability

An Examination of Foundations

Author: Terrence L. Fine

Publisher: Academic Press

ISBN: 1483263894

Category: Mathematics

Page: 276

View: 5624

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.
Posted in Mathematics

Foundations of Probability

Author: Alfred Renyi

Publisher: Courier Corporation

ISBN: 0486462617

Category: Mathematics

Page: 366

View: 4889

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.
Posted in Mathematics

Proceedings of the Conference Foundations of Probability and Physics

Vaxjo, Sweden, 25 November-1 December 2000

Author: A. Khrennikov

Publisher: World Scientific

ISBN: 9789812810809

Category: Electronic books

Page: 377

View: 8729

In this volume, leading experts in experimental as well as theoretical physics (both classical and quantum) and probability theory give their views on many intriguing (and still mysterious) problems regarding the probabilistic foundations of physics. The problems discussed during the conference include EinsteinOCoPodolskyOCoRosen paradox, Bell's inequality, realism, nonlocality, role of Kolmogorov model of probability theory in quantum physics, von Mises frequency theory, quantum information, computation, OC quantum effectsOCO in classical physics. Contents: Locality and Bell's Inequality (L Accardi & M Regoli); Refutation of Bell's Theorem (G Adenier); Forcing Discretization and Determination in Quantum History Theories (B Coecke); Some Remarks on Hardy Functions Associated with Dirichlet Series (W Ehm); Ensemble Probabilistic Equilibrium and Non-Equilibrium Thermodynamics without the Thermodynamic Limit (D H E Gross); An Approach to Quantum Probability (S Gudder); Innovation Approach to Stochastic Processes and Quantum Dynamics (T Hida); Origin of Quantum Probabilities (A Khrennikov); OC ComplementarityOCO or Schizophrenia: Is Probability in Quantum Mechanics Information or Onta? (A F Kracklauer); A Probabilistic Inequality for the KochenOCoSpecker Paradox (J-A Larsson); Quantum Stochastics. The New Approach to the Description of Quantum Measurements (E Loubenets); Is Random Event a Core Question? Some Remarks and a Proposal (P Rocchi); Quantum Cryptography in Space and Bell's Theorem (I Volovich); and other papers. Readership: Graduate students and researchers in quantum physics, mathematical physics, theoretical physics, stochastic processes, and probability & statistics."
Posted in Electronic books

The Logic of Chance

An Essay on the Foundations and Province of the Theory of Probability, with Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science

Author: John Venn

Publisher: N.A

ISBN: N.A

Category: Chance

Page: 488

View: 6151

Posted in Chance

The Foundations of Statistics

Author: Leonard J. Savage

Publisher: Courier Corporation

ISBN: 0486137104

Category: Mathematics

Page: 352

View: 5730

Classic analysis of the foundations of statistics and development of personal probability, one of the greatest controversies in modern statistical thought. Revised edition. Calculus, probability, statistics, and Boolean algebra are recommended.
Posted in Mathematics

Mathematical Foundations of Statistical Mechanics

Author: Aleksandr I?Akovlevich Khinchin

Publisher: Courier Corporation

ISBN: 9780486601472

Category: Mathematics

Page: 179

View: 3678

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.
Posted in Mathematics

Theory of Probability

A Critical Introductory Treatment

Author: Bruno de Finetti

Publisher: John Wiley & Sons

ISBN: 1119286379

Category: Mathematics

Page: 596

View: 3184

First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics. De Finetti’s theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something will happen and that that probability does not exist outside the mind. It is the rate at which a person is willing to bet on something happening. This view is directly opposed to the classicist/ frequentist view of the likelihood of a particular outcome of an event, which assumes that the same event could be identically repeated many times over, and the 'probability' of a particular outcome has to do with the fraction of the time that outcome results from the repeated trials.
Posted in Mathematics

Nomic Probability and the Foundations of Induction

Author: John L. Pollock

Publisher: Oxford University Press

ISBN: 9780195345216

Category: Mathematics

Page: 368

View: 8819

In this book Pollock deals with the subject of probabilistic reasoning, making general philosophical sense of objective probabilities and exploring their relationship to the problem of induction. He argues that probability is fundamental not only to physical science, but to induction, epistemology, the philosophy of science and much of the reasoning relevant to artificial intelligence. Pollock's main claim is that the fundamental notion of probability is nomic--that is, it involves the notion of natural law, valid across possible worlds. The various epistemic and statistical conceptions of probability, he demonstrates, are derived from this nomic notion. He goes on to provide a theory of statistical induction, an account of computational principles allowing some probabilities to be derived from others, an account of acceptance rules, and a theory of direct inference.
Posted in Mathematics

Theories of Probability

An Examination of Logical and Qualitative Foundations

Author: Louis Narens

Publisher: World Scientific

ISBN: 9812708014

Category: Mathematics

Page: 219

View: 5087

Standard probability theory has been an enormously successful contribution to modern science. However, from many perspectives it is too narrow as a general theory of uncertainty, particularly for issues involving subjective uncertainty. This first-of-its-kind book is primarily based on qualitative approaches to probabilistic-like uncertainty, and includes qualitative theories for the standard theory as well as several of its generalizations.One of these generalizations produces a belief function composed of two functions: a probability function that measures the probabilistic strength of an uncertain event, and another function that measures the amount of ambiguity or vagueness of the event. Another unique approach of the book is to change the event space from a boolean algebra, which is closely linked to classical propositional logic, to a different event algebra that is closely linked to a well-studied generalization of classical propositional logic known as intuitionistic logic. Together, these new qualitative theories succeed where the standard probability theory fails by accounting for a number of puzzling empirical findings in the psychology of human probability judgments and decision making.
Posted in Mathematics

Probability Theory

Author: Alfred Renyi

Publisher: Courier Corporation

ISBN: 0486458679

Category: Mathematics

Page: 666

View: 9598

The founder of Hungary's Probability Theory School, A. Rényi made significant contributions to virtually every area of mathematics. This introductory text is the product of his extensive teaching experience and is geared toward readers who wish to learn the basics of probability theory, as well as those who wish to attain a thorough knowledge in the field. Based on the author's lectures at the University of Budapest, this text requires no preliminary knowledge of probability theory. Readers should, however, be familiar with other branches of mathematics, including a thorough understanding of the elements of the differential and integral calculus and the theory of real and complex functions. These well-chosen problems and exercises illustrate the algebras of events, discrete random variables, characteristic functions, and limit theorems. The text concludes with an extensive appendix that introduces information theory.
Posted in Mathematics

Foundations of Modern Probability

Author: Olav Kallenberg

Publisher: Springer Science & Business Media

ISBN: 0387227040

Category: Mathematics

Page: 523

View: 5283

Unique for its broad and yet comprehensive coverage of modern probability theory, ranging from first principles and standard textbook material to more advanced topics. In spite of the economical exposition, careful proofs are provided for all main results. After a detailed discussion of classical limit theorems, martingales, Markov chains, random walks, and stationary processes, the author moves on to a modern treatment of Brownian motion, L=82vy processes, weak convergence, It=93 calculus, Feller processes, and SDEs. The more advanced parts include material on local time, excursions, and additive functionals, diffusion processes, PDEs and potential theory, predictable processes, and general semimartingales. Though primarily intended as a general reference for researchers and graduate students in probability theory and related areas of analysis, the book is also suitable as a text for graduate and seminar courses on all levels, from elementary to advanced. Numerous easy to more challenging exercises are provided, especially for the early chapters. From the author of "Random Measures".
Posted in Mathematics

The Theory of Probability

An Inquiry Into the Logical and Mathematical Foundations of the Calculus of Probability

Author: Hans Reichenbach

Publisher: Univ of California Press

ISBN: 9780520019294

Category: Logic, Symbolic and mathematical

Page: 492

View: 8680

Posted in Logic, Symbolic and mathematical

Truth, Possibility and Probability

New Logical Foundations of Probability and Statistical Inference

Author: R. Chuaqui

Publisher: Elsevier

ISBN: 9780080872773

Category: Mathematics

Page: 483

View: 5521

Anyone involved in the philosophy of science is naturally drawn into the study of the foundations of probability. Different interpretations of probability, based on competing philosophical ideas, lead to different statistical techniques, and frequently to mutually contradictory consequences. This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries. Mathematical models are constructed based on this interpretation, and statistical inference and decision theory are applied, including some examples in artificial intelligence, solving the main foundational problems. Nonstandard analysis is extensively developed for the construction of the models and in some of the proofs. Many nonstandard theorems are proved, some of them new, in particular, a representation theorem that asserts that any stochastic process can be approximated by a process defined over a space with equiprobable outcomes.
Posted in Mathematics

The Foundations of Causal Decision Theory

Author: James M. Joyce

Publisher: Cambridge University Press

ISBN: 1139471384

Category: Science

Page: N.A

View: 1852

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available.
Posted in Science

Foundations of the Probabilistic Mechanics of Discrete Media

Author: D. R. Axelrad

Publisher: Elsevier

ISBN: 1483285723

Category: Science

Page: 174

View: 1642

This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of such variables. Hence the probabilistic mechanics of discrete media are based on the mathematical theory of probability and the axiomatics of measure theory.
Posted in Science

Probability Foundations of Economic Theory

Author: Charles McCann

Publisher: Routledge

ISBN: 1134839138

Category: Business & Economics

Page: 188

View: 2625

First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.
Posted in Business & Economics

Foundations of Probability with Applications

Selected Papers 1974-1995

Author: Patrick Suppes,Mario Zanotti

Publisher: Cambridge University Press

ISBN: 9780521568357

Category: Mathematics

Page: 193

View: 8087

This is an important collection of essays by a leading philosopher, dealing with the foundations of probability.
Posted in Mathematics

Foundations and Philosophy of Epistemic Applications of Probability Theory

Author: W.L. Harper,Cliff Hooker

Publisher: Springer Science & Business Media

ISBN: 9789027706171

Category: Philosophy

Page: 308

View: 9218

Proceedings of an International Research Colloquium held at the University of Western Ontario, 10-13 May 1973.
Posted in Philosophy