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.
Author(s): Sheldon M. Ross, Erol A. Peköz
Edition: 2
Publisher: Cambridge University Press
Year: 2023
Language: English
Commentary: Second Edition 2023 (Version 2, July 2023)
Pages: 196
City: Cambridge
Tags: Probabilities; Measure Theory; Large Numbers Laws; Stein’s Method; Central Limit Theorems; Markov Chains; Renewal Theory; Brownian Motion
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.
