Probability: An Introduction Through Theory and Exercises (Universitext) - Softcover

Baldi, Paolo

Softcover

ISBN 10: 3031384911 ISBN 13: 9783031384912

Publisher: Springer, 2024

Synopsis

This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.

The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable forguided self-study.

Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic.

About this title

About the Author

Paolo Baldi is professor at the University of Rome "Tor Vergata". He previously held positions at the universities of Catania and Pisa in Italy and also many visiting positions at the universities of Nanterre and Pierre et Marie Curie (now Sorbonne Université) in France. The author of more than 50 journal articles and 6 books (mainly textbooks), his research has focused on stochastic processes, in particular stochastic modeling on algebraic and geometric structures, as well as large deviations and numerical applications.

From the Back Cover

This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.

The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study.

Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic.

Edition details

• Publisher: Springer
• Publication date: 2024
• Language: English
• ISBN 10: 3031384911
• ISBN 13: 9783031384912
• Binding: Paperback
• Edition number: 1
• Number of pages: 398