Advanced Probability Theory

A classic description of probability theory, which remains the proven work in the field.

The 2006 INFORMS Expository Writing Award-winning and best-selling author Sheldon Ross (University of Southern California) teams up with Erol Peköz (Boston University) to bring you this textbook for undergraduate and graduate students in statistics, mathematics, engineering, finance, and actuarial science. This is a guided tour designed to give familiarity with advanced topics in probability without having to wade through the exhaustive coverage of the classic advanced probability theory books. Topics 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 advanced topics rigorously but at such an accessible level; all you need is calculus and material from a first undergraduate course in probability.

A classic description of probability theory, which remains the proven work in the field.
This book is a revised and extended translation of a Swedish textbook which was published first in 1926 and then in entirely rewritten form in 1949. Starting with a historical introduction to the subjcct, the book covers the elements of the mathematical theory of probability, with the main emphasis on the theory of random variables and probability distributions. Applications to various fields, particularly to modern statistical methods, arc discusscd and illustrated by a number of examples. The problems offered for the reader's solution include simple exercises as well as important complements to the theories and methods given in the text.