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Author: Jan von Plato
Publisher: Cambridge University Press
Published: 1998-01-12
Total Pages: 336
ISBN-13: 9780521597357
DOWNLOAD EBOOKIn this book the author charts the history and development of modern probability theory.
Author: S. R. S. Varadhan
Publisher: American Mathematical Soc.
Published: 2001-09-10
Total Pages: 178
ISBN-13: 0821828525
DOWNLOAD EBOOKThis volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation. In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Then both the weak and strong limit theorems for sums of independent random variables are proved, including the weak and strong laws of large numbers, central limit theorems, laws of the iterated logarithm, and the Kolmogorov three series theorem. The first part concludes with infinitely divisible distributions and limit theorems for sums of uniformly infinitesimal independent random variables. The second part of the book mainly deals with dependent random variables, particularly martingales and Markov chains. Topics include standard results regarding discrete parameter martingales and Doob's inequalities. The standard topics in Markov chains are treated, i.e., transience, and null and positive recurrence. A varied collection of examples is given to demonstrate the connection between martingales and Markov chains. Additional topics covered in the book include stationary Gaussian processes, ergodic theorems, dynamic programming, optimal stopping, and filtering. A large number of examples and exercises is included. The book is a suitable text for a first-year graduate course in probability.
Author: Rick Durrett
Publisher: Cambridge University Press
Published: 2010-08-30
Total Pages:
ISBN-13: 113949113X
DOWNLOAD EBOOKThis 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:
Publisher: Allied Publishers
Published: 2013
Total Pages: 436
ISBN-13: 9788177644517
DOWNLOAD EBOOKProbability theory
Author: Michael Havbro Faber
Publisher: Springer Science & Business Media
Published: 2012-03-26
Total Pages: 198
ISBN-13: 9400740557
DOWNLOAD EBOOKThis book provides the reader with the basic skills and tools of statistics and probability in the context of engineering modeling and analysis. The emphasis is on the application and the reasoning behind the application of these skills and tools for the purpose of enhancing decision making in engineering. The purpose of the book is to ensure that the reader will acquire the required theoretical basis and technical skills such as to feel comfortable with the theory of basic statistics and probability. Moreover, in this book, as opposed to many standard books on the same subject, the perspective is to focus on the use of the theory for the purpose of engineering model building and decision making. This work is suitable for readers with little or no prior knowledge on the subject of statistics and probability.
Author: Edward Nelson
Publisher: Princeton University Press
Published: 1987
Total Pages: 112
ISBN-13: 9780691084749
DOWNLOAD EBOOKUsing only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
Author: James Jaccard
Publisher: Guilford Publications
Published: 2020-02-06
Total Pages: 545
ISBN-13: 1462542441
DOWNLOAD EBOOK"This book provides young scientists with tools to assist them in the practical aspects of theory construction. We take an informal journey through the cognitive heuristics, tricks of the trade, and ways of thinking that we have found to be useful in developing theories-essentially, conceptualizations-that can advance knowledge in the social sciences. This book is intended to provide the instructor with a useful source for helping students come up with ideas for research and for fine-tuning the resultant theories that emerge from such thinking. An objective of this book is to move toward a needed balance in the emphases given to theory construction and theory testing"--
Author: Pamela J. Shoemaker
Publisher: SAGE Publications
Published: 2003-12-10
Total Pages: 241
ISBN-13: 1452210438
DOWNLOAD EBOOKClick ′Additional Materials′ to read the foreword by Jerald Hage As straightforward as its title, How to Build Social Science Theories sidesteps the well-traveled road of theoretical examination by demonstrating how new theories originate and how they are elaborated. Essential reading for students of social science research, this book traces theories from their most rudimentary building blocks (terminology and definitions) through multivariable theoretical statements, models, the role of creativity in theory building, and how theories are used and evaluated. Authors Pamela J. Shoemaker, James William Tankard, Jr., and Dominic L. Lasorsa intend to improve research in many areas of the social sciences by making research more theory-based and theory-oriented. The book begins with a discussion of concepts and their theoretical and operational definitions. It then proceeds to theoretical statements, including hypotheses, assumptions, and propositions. Theoretical statements need theoretical linkages and operational linkages; this discussion begins with bivariate relationships, as well as three-variable, four-variable, and further multivariate relationships. The authors also devote chapters to the creative component of theory-building and how to evaluate theories. How to Build Social Science Theories is a sophisticated yet readable analysis presented by internationally known experts in social science methodology. It is designed primarily as a core text for graduate and advanced undergraduate courses in communication theory. It will also be a perfect addition to any course dealing with theory and research methodology across the social sciences. Additionally, professional researchers will find it an indispensable guide to the genesis, dissemination, and evaluation of social science theories.
Author: David F. Anderson
Publisher: Cambridge University Press
Published: 2017-11-02
Total Pages: 447
ISBN-13: 110824498X
DOWNLOAD EBOOKThis classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Author: R. M. Dudley
Publisher: CRC Press
Published: 2018-02-01
Total Pages: 479
ISBN-13: 1351093096
DOWNLOAD EBOOKWritten by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory.
