A Modern Approach To Probability Theory

Author : Bert E. Fristedt,Lawrence F. Gray
Publisher : Springer Science & Business Media
Page : 775 pages
File Size : 42,9 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781489928375

Get Book

A Modern Approach to Probability Theory by Bert E. Fristedt,Lawrence F. Gray Pdf

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.

Author : F.M. Dekking,C. Kraaikamp,H.P. Lopuhaä,L.E. Meester
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 49,7 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9781846281686

Get Book

A Modern Introduction to Probability and Statistics by F.M. Dekking,C. Kraaikamp,H.P. Lopuhaä,L.E. Meester Pdf

Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

Author : Morris Hamburg
Publisher : Houghton Mifflin Harcourt P
Page : 520 pages
File Size : 41,8 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015043001885

Get Book

Basic Statistics by Morris Hamburg Pdf

Statistical investigations and data; Frequency distributions and summary measures; Introduction to probability; Probability distributions; Estimation; Hypothesis testing; Chi-square tests and analysis of variance; Regression and correlation analysis; Nonparametric statistics; Decision making under uncertainty; Time series; Index numbers.

Author : B. Ramdas Bhat
Publisher : Unknown
Page : 296 pages
File Size : 45,7 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015015627550

Get Book

Modern Probability Theory by B. Ramdas Bhat Pdf

A comprehensive treatment, unique in covering probability theory independently of modern theory. New edition features additional problems, examples that show scope and limitations of various results, and enlarged chapters on laws of large numbers, extensions, and generalizations.

Author : Nima Moshayedi
Publisher : World Scientific
Page : 292 pages
File Size : 54,6 Mb
Release : 2022-03-23
Category : Mathematics
ISBN : 9789811243363

Get Book

Introduction To Probability Theory: A First Course On The Measure-theoretic Approach by Nima Moshayedi Pdf

This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it.The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability language. The second part is devoted to some more sophisticated methods such as conditional expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part. /description --

Author : B. Ramdas Bhat
Publisher : Unknown
Page : 256 pages
File Size : 52,8 Mb
Release : 1981
Category : Probabilities
ISBN : 085226061X

Get Book

Modern Probability Theory by B. Ramdas Bhat Pdf

Author : Emanuel Parzen
Publisher : Unknown
Page : 666 pages
File Size : 50,9 Mb
Release : 1960
Category : Probabilities
ISBN : UOM:39015012010628

Get Book

Modern Probability Theory and Its Applications by Emanuel Parzen Pdf

Author : Jeffrey S Rosenthal
Publisher : World Scientific Publishing Company
Page : 236 pages
File Size : 47,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9789813101654

Get Book

First Look At Rigorous Probability Theory, A (2nd Edition) by Jeffrey S Rosenthal Pdf

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 : Olav Kallenberg
Publisher : Springer Science & Business Media
Page : 523 pages
File Size : 44,8 Mb
Release : 2006-05-10
Category : Mathematics
ISBN : 9780387227047

Get Book

Foundations of Modern Probability by Olav Kallenberg Pdf

Unique for its broad and yet comprehensive coverage of modern probability theory, ranging from first principles and standard textbook material to more advanced topics. In spite of the economical exposition, careful proofs are provided for all main results. After a detailed discussion of classical limit theorems, martingales, Markov chains, random walks, and stationary processes, the author moves on to a modern treatment of Brownian motion, L=82vy processes, weak convergence, It=93 calculus, Feller processes, and SDEs. The more advanced parts include material on local time, excursions, and additive functionals, diffusion processes, PDEs and potential theory, predictable processes, and general semimartingales. Though primarily intended as a general reference for researchers and graduate students in probability theory and related areas of analysis, the book is also suitable as a text for graduate and seminar courses on all levels, from elementary to advanced. Numerous easy to more challenging exercises are provided, especially for the early chapters. From the author of "Random Measures".

Author : Jeffrey S. Rosenthal
Publisher : World Scientific
Page : 200 pages
File Size : 48,5 Mb
Release : 2000
Category : Mathematics
ISBN : 9810243227

Get Book

A First Look at Rigorous Probability Theory by Jeffrey S. Rosenthal Pdf

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 : Vladas Sidoravicius
Publisher : Springer Nature
Page : 341 pages
File Size : 40,7 Mb
Release : 2019-10-17
Category : Mathematics
ISBN : 9789811503023

Get Book

Sojourns in Probability Theory and Statistical Physics - III by Vladas Sidoravicius Pdf

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Author : Rick Durrett
Publisher : Cambridge University Press
Page : 128 pages
File Size : 53,5 Mb
Release : 2010-08-30
Category : Mathematics
ISBN : 9781139491136

Get Book

Probability by Rick Durrett Pdf

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 : Marcelo S. Alencar,Valdemar C. da Rocha
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 52,8 Mb
Release : 2005-08-23
Category : Technology & Engineering
ISBN : 0387254811

Get Book

Communication Systems by Marcelo S. Alencar,Valdemar C. da Rocha Pdf

Presents main concepts of mobile communication systems, both analog and digital Introduces concepts of probability, random variables and stochastic processes and their applications to the analysis of linear systems Includes five appendices covering Fourier series and transforms, GSM cellular systems and more

Author : Marcelo S. Alencar,Raphael T. Alencar
Publisher : CRC Press
Page : 303 pages
File Size : 49,9 Mb
Release : 2024-03-12
Category : Mathematics
ISBN : 9781003808954

Get Book

Set, Measure and Probability Theory by Marcelo S. Alencar,Raphael T. Alencar Pdf

This book introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random variables, convergence theorems, laws of large numbers, and fundamental inequalities. The idea is to present a seamless connection between the more abstract advanced set theory, the fundamental concepts from measure theory, and integration, to introduce the axiomatic theory of probability, filling in the gaps from previous books and leading to an interesting, robust and, hopefully, self-contained exposition of the theory. This book also presents an account of the historical evolution of probability theory as a mathematical discipline. Each chapter presents a short biography of the important scientists who helped develop the subject. Appendices include Fourier transforms in one and two dimensions, important formulas and inequalities and commented bibliography. Many examples, illustrations and graphics help the reader understand the theory.

Author : Marc Yor
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 42,9 Mb
Release : 1997-03-20
Category : Mathematics
ISBN : 3764357177

Get Book

Some Aspects of Brownian Motion by Marc Yor Pdf

The following notes represent approximately the second half of the lectures I gave in the Nachdiplomvorlesung, in ETH, Zurich, between October 1991 and February 1992, together with the contents of six additional lectures I gave in ETH, in November and December 1993. Part I, the elder brother of the present book [Part II], aimed at the computation, as explicitly as possible, of a number of interesting functionals of Brownian motion. It may be natural that Part II, the younger brother, looks more into the main technique with which Part I was "working", namely: martingales and stochastic calculus. As F. Knight writes, in a review article on Part I, in which research on Brownian motion is compared to gold mining: "In the days of P. Levy, and even as late as the theorems of "Ray and Knight" (1963), it was possible for the practiced eye to pick up valuable reward without the aid of much technology . . . Thereafter, however, the rewards are increasingly achieved by the application of high technology". Although one might argue whether this golden age is really foregone, and discuss the "height" of the technology involved, this quotation is closely related to the main motivations of Part II: this technology, which includes stochastic calculus for general discontinuous semi-martingales, enlargement of filtrations, . . .