A First Look at Rigorous Probability Theory

Second Edition
Author: Jeffrey S Rosenthal
Publisher: World Scientific Publishing Company
ISBN: 9813101652
Category: Mathematics
Page: 236
View: 4591

Continue Reading →

Solutions Manual for Free Download 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.

A First Look at Rigorous Probability Theory


Author: Jeffrey S Rosenthal
Publisher: World Scientific Publishing Company
ISBN: 9813105704
Category:
Page: 192
View: 7701

Continue Reading →

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. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.

A First Look at Rigorous Probability Theory


Author: Jeffrey S. Rosenthal
Publisher: World Scientific
ISBN: 9789810243227
Category: Mathematics
Page: 177
View: 6204

Continue Reading →

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.

Probability with Martingales


Author: David Williams
Publisher: Cambridge University Press
ISBN: 1139642987
Category: Mathematics
Page: N.A
View: 567

Continue Reading →

Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. A distinguishing feature is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals; and it assumes certain key results from measure theory in the main text. These measure-theoretic results are proved in full in appendices, so that the book is completely self-contained. The book is written for students, not for researchers, and has evolved through several years of class testing. Exercises play a vital rôle. Interesting and challenging problems, some with hints, consolidate what has already been learnt, and provide motivation to discover more of the subject than can be covered in a single introduction.

Elementary Probability Theory with Stochastic Processes


Author: K. L. Chung
Publisher: Springer Science & Business Media
ISBN: 1475751141
Category: Mathematics
Page: 325
View: 1344

Continue Reading →

In the past half-century the theory of probability has grown from a minor isolated theme into a broad and intensive discipline interacting with many other branches of mathematics. At the same time it is playing a central role in the mathematization of various applied sciences such as statistics, opera tions research, biology, economics and psychology-to name a few to which the prefix "mathematical" has so far been firmly attached. The coming-of-age of probability has been reflected in the change of contents of textbooks on the subject. In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution. This period ended with the appearance of Feller's classic treatise (see [Feller l]t) in 1950, from the manuscript of which I gave my first substantial course in probability. With the passage of time probability theory and its applications have won a place in the college curriculum as a mathematical discipline essential to many fields of study. The elements of the theory are now given at different levels, sometimes even before calculus. The present textbook is intended for a course at about the sophomore level. It presupposes no prior acquaintance with the subject and the first three chapters can be read largely without the benefit of calculus.

Measure, Integral and Probability


Author: Marek Capinski,(Peter) Ekkehard Kopp
Publisher: Springer Science & Business Media
ISBN: 1447136314
Category: Mathematics
Page: 227
View: 9316

Continue Reading →

This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

An Intermediate Course in Probability


Author: Allan Gut
Publisher: Springer Science & Business Media
ISBN: 1441901620
Category: Mathematics
Page: 303
View: 6382

Continue Reading →

This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory. There is no competitor to this book. The book can be used in classrooms as well as for self-study.

Measure Theory and Probability Theory


Author: Krishna B. Athreya,Soumendra N. Lahiri
Publisher: Springer Science & Business Media
ISBN: 038732903X
Category: Business & Economics
Page: 618
View: 455

Continue Reading →

This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended primarily for first year Ph.D. students in mathematics and statistics although mathematically advanced students from engineering and economics would also find the book useful. Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms. Thus part I would be particularly useful for students in a typical Statistics Ph.D. program if a separate course on real analysis is not a standard requirement. Part II (chapters 6-13) provides full coverage of standard graduate level probability theory. It starts with Kolmogorov's probability model and Kolmogorov's existence theorem. It then treats thoroughly the laws of large numbers including renewal theory and ergodic theorems with applications and then weak convergence of probability distributions, characteristic functions, the Levy-Cramer continuity theorem and the central limit theorem as well as stable laws. It ends with conditional expectations and conditional probability, and an introduction to the theory of discrete time martingales. Part III (chapters 14-18) provides a modest coverage of discrete time Markov chains with countable and general state spaces, MCMC, continuous time discrete space jump Markov processes, Brownian motion, mixing sequences, bootstrap methods, and branching processes. It could be used for a topics/seminar course or as an introduction to stochastic processes. Krishna B. Athreya is a professor at the departments of mathematics and statistics and a Distinguished Professor in the College of Liberal Arts and Sciences at the Iowa State University. He has been a faculty member at University of Wisconsin, Madison; Indian Institute of Science, Bangalore; Cornell University; and has held visiting appointments in Scandinavia and Australia. He is a fellow of the Institute of Mathematical Statistics USA; a fellow of the Indian Academy of Sciences, Bangalore; an elected member of the International Statistical Institute; and serves on the editorial board of several journals in probability and statistics. Soumendra N. Lahiri is a professor at the department of statistics at the Iowa State University. He is a fellow of the Institute of Mathematical Statistics, a fellow of the American Statistical Association, and an elected member of the International Statistical Institute.

A Modern Approach to Probability Theory


Author: Bert E. Fristedt,Lawrence F. Gray
Publisher: Springer Science & Business Media
ISBN: 1489928375
Category: Mathematics
Page: 758
View: 9733

Continue Reading →

Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

Concepts of Probability Theory

Second Revised Edition
Author: Paul E. Pfeiffer
Publisher: Courier Corporation
ISBN: 0486165663
Category: Mathematics
Page: 416
View: 8020

Continue Reading →

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.

Struck by Lightning:

The Curious World of Probabilities
Author: Jeffrey S. Rosenthal
Publisher: National Academies Press
ISBN: 9780309097345
Category: Science
Page: 270
View: 9870

Continue Reading →

From terrorist attacks to big money jackpots, Struck by Lightning deconstructs the odds and oddities of chance, examining both the relevant and irreverent role of randomness in our everyday lives. Human beings have long been both fascinated and appalled by randomness. On the one hand, we love the thrill of a surprise party, the unpredictability of a budding romance, or the freedom of not knowing what tomorrow will bring. We are inexplicably delighted by strange coincidences and striking similarities. But we also hate uncertainty's dark side. From cancer to SARS, diseases strike with no apparent pattern. Terrorists attack, airplanes crash, bridges collapse, and we never know if we'll be that one in a million statistic. We are all constantly faced with situations and choices that involve randomness and uncertainty. A basic understanding of the rules of probability theory, applied to real-life circumstances, can help us to make sense of these situations, to avoid unnecessary fear, to seize the opportunities that randomness presents to us, and to actually enjoy the uncertainties we face. The reality is that when it comes to randomness, you can run, but you can't hide. So many aspects of our lives are governed by events that are simply not in our control. In this entertaining yet sophisticated look at the world of probabilities, author Jeffrey Rosenthal--an improbably talented math professor--explains the mechanics of randomness and teaches us how to develop an informed perspective on probability.

A Probability Path


Author: Sidney Resnick
Publisher: Springer Science & Business Media
ISBN: 9780817640552
Category: Mathematics
Page: 453
View: 383

Continue Reading →

Many probability books are written by mathematicians and have the built in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.

Probability and Measure Theory


Author: Robert B. Ash,Catherine Doléans-Dade
Publisher: Academic Press
ISBN: 9780120652020
Category: Mathematics
Page: 516
View: 1486

Continue Reading →

Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion. * Clear, readable style * Solutions to many problems presented in text * Solutions manual for instructors * Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics * No knowledge of general topology required, just basic analysis and metric spaces * Efficient organization

Advanced Probability Theory, Second Edition,


Author: Janos Galambos
Publisher: CRC Press
ISBN: 9780824793326
Category: Mathematics
Page: 480
View: 9672

Continue Reading →

This work thoroughly covers the concepts and main results of probability theory, from its fundamental principles to advanced applications. This edition provides examples early in the text of practical problems such as the safety of a piece of engineering equipment or the inevitability of wrong conclusions in seemingly accurate medical tests for AIDS and cancer.;College or university bookstores may order five or more copies at a special student price which is available upon request from Marcel Dekker, Inc.

Probability Essentials


Author: Jean Jacod,Philip Protter
Publisher: Springer Science & Business Media
ISBN: 3642556825
Category: Mathematics
Page: 254
View: 2553

Continue Reading →

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.

Probability and Statistics

The Science of Uncertainty
Author: Michael J. Evans,Jeffrey S. Rosenthal
Publisher: Macmillan
ISBN: 9780716747420
Category: Mathematics
Page: 685
View: 2444

Continue Reading →

Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.

A Natural Introduction to Probability Theory


Author: R. Meester
Publisher: Springer Science & Business Media
ISBN: 9783764387242
Category: Mathematics
Page: 198
View: 1377

Continue Reading →

Compactly written, but nevertheless very readable, appealing to intuition, this introduction to probability theory is an excellent textbook for a one-semester course for undergraduates in any direction that uses probabilistic ideas. Technical machinery is only introduced when necessary. The route is rigorous but does not use measure theory. The text is illustrated with many original and surprising examples and problems taken from classical applications like gambling, geometry or graph theory, as well as from applications in biology, medicine, social sciences, sports, and coding theory. Only first-year calculus is required.

A Basic Course in Measure and Probability

Theory for Applications
Author: Ross Leadbetter,Stamatis Cambanis,Vladas Pipiras
Publisher: Cambridge University Press
ISBN: 1107020409
Category: Mathematics
Page: 376
View: 1959

Continue Reading →

A concise introduction covering all of the measure theory and probability most useful for statisticians.

The Theory of Probability

Explorations and Applications
Author: Santosh S. Venkatesh
Publisher: Cambridge University Press
ISBN: 1107024471
Category: Mathematics
Page: 805
View: 8901

Continue Reading →

From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.

Probability and measure


Author: Patrick Billingsley
Publisher: John Wiley & Sons Inc
ISBN: N.A
Category: Mathematics
Page: 622
View: 2281

Continue Reading →

Like the previous editions, this new edition will be well received by students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.