This book is intended as a text for graduate students and as a reference for workers in probability and statistics. The prerequisite is honest calculus. The material covered in Parts Two to Five inclusive requires about three to four semesters of graduate study. The introductory part may serve as a text for an undergraduate course in elementary probability theory. Numerous historical marks about results, methods, and the evolution of various fields are an intrinsic part of the text. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated.

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.

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.

This fourth edition contains several additions. The main ones con cern three closely related topics: Brownian motion, functional limit distributions, and random walks. Besides the power and ingenuity of their methods and the depth and beauty of their results, their importance is fast growing in Analysis as well as in theoretical and applied Proba bility. These additions increased the book to an unwieldy size and it had to be split into two volumes. About half of the first volume is devoted to an elementary introduc tion, then to mathematical foundations and basic probability concepts and tools. The second half is devoted to a detailed study of Independ ence which played and continues to playa central role both by itself and as a catalyst. The main additions consist of a section on convergence of probabilities on metric spaces and a chapter whose first section on domains of attrac tion completes the study of the Central limit problem, while the second one is devoted to random walks. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated. The main addition consists of a chapter on Brownian motion and limit distributions.

Probability theory

Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.

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.

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.

This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.

This comprehensive presentation of the basic concepts of probability theory examines both classical and modern methods. The treatment emphasizes the relationship between probability theory and mathematical analysis, and it stresses applications to statistics as well as to analysis. Topics include: • The laws of large numbers • Distribution and characteristic functions • The central limit problem • Dependence • Random variables taking values in a normed linear space Each chapter features worked examples in addition to problems, and bibliographical references to supplementary reading material enhance the text. For advanced undergraduates and graduate students in mathematics.