Probability : theory and examples
 Responsibility
 Rick Durrett (Duke University, Durham, North Carolina)
 Edition
 Fifth edition
 Publication
 Cambridge ; New York, NY : Cambridge University Press, 2019
 Physical description
 1 online resource
 Series
 Cambridge series on statistical and probabilistic mathematics ; 49.
Online
Course reserve
 Course
 MATH230B01  Theory of Probability
 Instructor(s)
 Dembo, Amir
 Course
 STATS310B01  Theory of Probability II
 Instructor(s)
 Dembo, Amir
More options
Description
Creators/Contributors
 Author/Creator
 Durrett, Richard, 1951 author.
 Contributor
 Cambridge University Press.
Contents/Summary
 Bibliography
 Includes bibliographical references and index
 Contents

 1. Measure theory
 2. Laws of large numbers
 3. Central limit theorems
 4. Martingales
 5. Markov chains
 6. Ergodic theorems
 7. Brownian motion
 8. Applications to random walk
 9. Multidimensional Brownian motion Appendix. Measure theory details.
 (source: Nielsen Book Data)
 Summary

This lively introduction to measuretheoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference. Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended examples that apply the theory to concrete applications. This fifth edition contains a new chapter on multidimensional Brownian motion and its relationship to partial differential equations (PDEs), an advanced topic that is finding new applications. Setting the foundation for this expansion, Chapter 7 now features a proof of Ito's formula. Key exercises that previously were simply proofs left to the reader have been directly inserted into the text as lemmas. The new edition reinstates discussion about the central limit theorem for martingales and stationary sequences.
(source: Nielsen Book Data)
Subjects
 Subject
 Probabilities.
 Probabilities > Textbooks.
Bibliographic information
 Publication date
 2019
 Series
 Cambridge series in statistical and probabilistic mathematics ; 49
 Reproduction
 Electronic reproduction. Cambridge Available via World Wide Web
 ISBN
 9781108591034 (electronic bk.)
 1108591035 (electronic bk.)
 9781108473682 (hardback)
 1108473687