This book explores probability theory as a companion to statistics, starting with fundamental tools and covering topics like inequalities, characteristic functions, and convergence. It delves into key concepts such as the law of large numbers and martingales, with updates and new references in this edition.
This book offers a thorough and rigorous exploration of probability theory, bridging the gap between undergraduate and graduate levels. It features numerous examples, exercises, and varied methods to solve problems, enhancing understanding and application of key concepts. Ideal for classroom use or self-study, it covers essential topics in pure probability theory.
The updated edition delves into the complexities of stopped random walks, featuring enhanced content and insights on future developments and generalizations in the field. A new chapter focuses on perturbed random walks, expanding the scope of the discussion. Additionally, nearly 100 new bibliographic references enrich the resource, making it a comprehensive guide for researchers and enthusiasts alike.
The book explores the theory of asymptotic martingales using a measure-theoretic framework, providing a comprehensive introduction to this advanced statistical concept. It delves into the properties and applications of asymptotic martingales, offering insights into their behavior and significance in probability theory. Additionally, the text includes a bibliography that serves as a valuable resource for further reading and research in the field, making it a useful reference for both students and professionals interested in advanced probability topics.