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Author: Jeffrey Seth Rosenthal
Publisher: World Scientific
Published: 2006
Total Pages: 238
ISBN-13: 9812703705
DOWNLOAD EBOOK →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
Published: 2019-09-26
Total Pages: 213
ISBN-13: 9811207925
DOWNLOAD EBOOK →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
Published: 2000
Total Pages: 200
ISBN-13: 9789810243227
DOWNLOAD EBOOK →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: Kai Lai Chung
Publisher: Springer Science & Business Media
Published: 2012-11-12
Total Pages: 411
ISBN-13: 0387215484
DOWNLOAD EBOOK →This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales. From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS
Author: George G. Roussas
Publisher: Gulf Professional Publishing
Published: 2005
Total Pages: 463
ISBN-13: 0125990227
DOWNLOAD EBOOK →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: Jean Jacod
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 247
ISBN-13: 3642556825
DOWNLOAD EBOOK →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: Robert B. Ash
Publisher: Courier Corporation
Published: 2008-06-26
Total Pages: 354
ISBN-13: 0486466280
DOWNLOAD EBOOK →This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus. Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.
Author: Ross Leadbetter
Publisher: Cambridge University Press
Published: 2014-01-30
Total Pages: 375
ISBN-13: 1107020409
DOWNLOAD EBOOK →A concise introduction covering all of the measure theory and probability most useful for statisticians.
Author: Santosh S. Venkatesh
Publisher: Cambridge University Press
Published: 2013
Total Pages: 830
ISBN-13: 1107024471
DOWNLOAD EBOOK →From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.
Author: David Pollard
Publisher: Cambridge University Press
Published: 2002
Total Pages: 372
ISBN-13: 9780521002899
DOWNLOAD EBOOK →This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
