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Author: Jeffrey Seth Rosenthal
Publisher: World Scientific
ISBN: 9812703705
Category : Mathematics
Languages : en
Pages : 238
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Book Description
Features an introduction to probability theory using measure theory. This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.
Author: Jeffrey Seth Rosenthal
Publisher: World Scientific
ISBN: 9812703705
Category : Mathematics
Languages : en
Pages : 238
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Book Description
Features an introduction to probability theory using measure theory. This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.
Author: Jeffrey S Rosenthal
Publisher: World Scientific
ISBN: 9811207925
Category : Mathematics
Languages : en
Pages : 213
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Book Description
This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.
Author: Jeffrey S Rosenthal
Publisher: World Scientific Publishing Company
ISBN: 9813101652
Category : Mathematics
Languages : en
Pages : 236
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Book Description
This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.
Author: George G. Roussas
Publisher: Gulf Professional Publishing
ISBN: 0125990227
Category : Computers
Languages : en
Pages : 463
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Book Description
This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics, probability and other related areas, should be equipped with. The approach is classical, avoiding the use of mathematical tools not necessary for carrying out the discussions. All proofs are presented in full detail. * Excellent exposition marked by a clear, coherent and logical devleopment of the subject * Easy to understand, detailed discussion of material * Complete proofs
Author: Olav Kallenberg
Publisher: Springer Science & Business Media
ISBN: 9780387953137
Category : Mathematics
Languages : en
Pages : 670
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Book Description
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.
Author: Jean Jacod
Publisher: Springer Science & Business Media
ISBN: 3642556825
Category : Mathematics
Languages : en
Pages : 247
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Book Description
This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.
Author: Jeffrey S. Rosenthal
Publisher: World Scientific
ISBN: 9789810243227
Category : Mathematics
Languages : en
Pages : 200
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Book Description
This textbook is an introduction to rigorous probability theory using measure theory. It provides rigorous, complete proofs of all the essential introductory mathematical results of probability theory and measure theory. More advanced or specialized areas are entirely omitted or only hinted at. For example, the text includes a complete proof of the classical central limit theorem, including the necessary continuity theorem for characteristic functions, but the more general Lindeberg central limit theorem is only outlined and is not proved. Similarly, all necessary facts from measure theory are proved before they are used, but more abstract or advanced measure theory results are not included. Furthermore, measure theory is discussed as much as possible purely in terms of probability, as opposed to being treated as a separate subject which must be mastered before probability theory can be understood.
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 113949113X
Category : Mathematics
Languages : en
Pages :
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Book Description
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Author: Wolfgang von der Linden
Publisher: Cambridge University Press
ISBN: 1107035902
Category : Mathematics
Languages : en
Pages : 653
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Book Description
Covering all aspects of probability theory, statistics and data analysis from a Bayesian perspective for graduate students and researchers.
Author: Charles Miller Grinstead
Publisher: American Mathematical Soc.
ISBN: 0821894145
Category : Mathematics
Languages : en
Pages : 530
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Book Description
This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject.
