About the Book
Written by Sheldon Ross and Erol Peköz, this text familiarises you with advanced topics in probability while keeping the mathematical prerequisites to a minimum. Topics covered include measure theory, limit theorems, bounding probabilities and expectations, coupling and Stein's method, martingales, Markov chains, renewal theory, and Brownian motion. No other text covers all these topics rigorously but at such an accessible level - all you need is an undergraduate-level understanding of calculus and probability. New to this edition are sections on the gambler's ruin problem, Stein's method as applied to exponential approximations, and applications of the martingale stopping theorem. Extra end-of-chapter exercises have also been added, with selected solutions available.This is an ideal textbook for students taking an advanced undergraduate or graduate course in probability. It also represents a useful resource for professionals in relevant application domains, from finance to machine learning.
Table of Contents:
Preface; 1. Measure Theory and Laws of Large Numbers; 2. Stein's Method and Central Limit Theorems; 3. Conditional Expectation and Martingales; 4. Bounding Probabilities and Expectations; 5. Markov Chains; 6. Renewal Theory; 7. Brownian Motion; References; Index.
About the Author :
Sheldon M. Ross is the Epstein Chair Professor in the Epstein Department of Industrial and Systems Engineering at the University of Southern California. He has published more than 150 technical articles as well as a variety of textbooks in the areas of applied probability, statistics, and industrial engineering. He is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences, a fellow of the Institute of Mathematical Statistics and of the Institute for Operations Research and the Management Sciences, and a recipient of the Humboldt US Senior Scientist Award. He is the recipient of the 2006 INFORMS Expository Writing Award. Erol A. Peköz is Professor and Department Chair of Operations and Technology Management in the Questrom School of Business at Boston University. He has published more than 50 technical articles in applied probability and statistics, and is the author of 'The Manager's Guide to Statistics' (2009). At Boston University, he was awarded the 2001 Broderick Prize for Teaching.
Review :
'A Second Course in Probability is a modern and concise introduction to advanced topics in probability and stochastic processes. This book stands out as one of the few at this level to cover Stein's method in an accessible way. It is an excellent reference for the reader who wants to learn how to prove distributional convergence and obtain explicit error bounds. Highly recommended!' Alessandro Arlotto, Duke University
'I've found A Second Course in Probability to be an invaluable resource for my graduate class in advanced probability theory for students pursuing statistics as their main research topic. The authors strike a good balance between technical detail and clarity of exposition, making this book an excellent choice for teaching the foundations of probability without distracting students with overly difficult technical details of the theory.' Adrian Röllin, National University of Singapore
'Profs. Ross and Pekoz have done a fabulous job of their intended purpose: to propose a streamlined textbook on rigorous probability theory which will help advanced undergraduates, graduate students, and professionals, in many fields of study, who need this understanding of the topics to work on their applied probability problems. This book contains just the right amount of measure-theoretic background to get these readers up to speed and able to understand, appreciate, and most importantly, implement rigorous probability modeling methods, largely free of hand-waving, and without insistence on mathematically sterile details. This is a well-executed balancing act.' Frederi Viens, Rice University
'This book is about probability and stochastic processes. It does not attempt to give an exhaustive treatment of the topics and is relatively selective in what it treats and how it treats it, which is quite refreshing, as there are already many texts that do provide a more exhaustive and traditional cover. It contains methods that are usually not common in standard texts and quite a few exercises. It is perfect for a more advanced course in probability and stochastic processes in any mathematical field, but especially for advanced undergraduate and graduate students in Statistics, Engineering, Finance and Actuarial Sciences. In addition to some standard topics that appear in most advanced probability and stochastic processes texts, this text contains chapters on Stein's method, probability and expectations bounds and renewal theory.' Offer Kella, The Hebrew University of Jerusalem
'This 2nd edition re-masters a measure-theoretic introduction to probability theory, including new sections on convergence, Stein's method for exponential distributions, and gambler's ruin, while being some 14 pages shorter than the original. The structure of the book and the progression of material in each of its seven chapters is even more condensed and carefully designed, keeping mathematical prerequisites to a minimum, while maintaining mathematical rigor hand in hand with the book's initial originality and intuitive appeal. A significant advantage of this book is that Chapter 1 develops the core of the theory swiftly and effectively, motivating the need for measurability in forming probability spaces, random variables, expected value, modes of stochastic convergence, 0-1 law and laws of large numbers. This is an ideal textbook for students taking an advanced undergraduate or graduate course in probability, and a useful resource for professionals in relevant application domains, from finance to machine learning.' Charalampos (Harry) Pavlopoulos, Athens University of Economics and Business
'This book, as the title suggests, is an excellent second read for learning probability. The set of covered topics is original, and deep results are explained, along with rigorous proofs, without losing the reader in too much theory. In addition, a profusion of interesting examples and exercises are provided alongside the chapters.' Olivier Lévêque, École Polytechnique Fédérale de Lausanne
