Author : Jeffrey Seth Rosenthal
Publisher : World Scientific
Page : 238 pages
File Size : 30,89 MB
Release : 2006
Category : Mathematics
ISBN : 9812703705
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
Page : 213 pages
File Size : 36,67 MB
Release : 2019-09-26
Category : Mathematics
ISBN : 9811207925
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
Page : 200 pages
File Size : 48,15 MB
Release : 2000
Category : Mathematics
ISBN : 9789810243227
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
Page : 411 pages
File Size : 36,74 MB
Release : 2012-11-12
Category : Mathematics
ISBN : 0387215484
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
Page : 463 pages
File Size : 37,1 MB
Release : 2005
Category : Computers
ISBN : 0125990227
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 : Jeffrey S Rosenthal
Publisher : World Scientific Publishing Company
Page : 236 pages
File Size : 16,51 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 9813101652
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 : René L. Schilling
Publisher : Cambridge University Press
Page : 404 pages
File Size : 22,20 MB
Release : 2005-11-10
Category : Mathematics
ISBN : 9780521850155
This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.
Author : Santosh S. Venkatesh
Publisher : Cambridge University Press
Page : 830 pages
File Size : 18,35 MB
Release : 2013
Category : Mathematics
ISBN : 1107024471
From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.
Author : Olav Kallenberg
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 20,83 MB
Release : 2002-01-08
Category : Mathematics
ISBN : 9780387953137
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Author : David Pollard
Publisher : Cambridge University Press
Page : 372 pages
File Size : 26,56 MB
Release : 2002
Category : Mathematics
ISBN : 9780521002899
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.
