Overview
- Written clearly to make complex mathematics accessible
- It provides many examples and solved exercises
- A rigorous, complete and self-contained presentation
Part of the book series: UNITEXT (UNITEXT, volume 165)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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Keywords
- Monte Carlo methods
- Law of large numbers
- Probability distribution
- Random variables
- Conditional probability
- Probability space
- Convergence of random variables
About this book
This book provides a concise yet rigorous introduction to probability theory. Among the possible approaches to the subject, the most modern approach based on measure theory has been chosen: although it requires a higher degree of mathematical abstraction and sophistication, it is essential to provide the foundations for the study of more advanced topics such as stochastic processes, stochastic differential calculus and statistical inference. The text originated from the teaching experience in probability and applied mathematics courses within the mathematics degree program at the University of Bologna; it is suitable for second- or third-year students in mathematics, physics, or other natural sciences, assuming multidimensional differential and integral calculus as a prerequisite. The four chapters cover the following topics: measures and probability spaces; random variables; sequences of random variables and limit theorems; and expectation and conditional distribution. The text includes a collection of solved exercises.
Authors and Affiliations
About the author
Andrea Pascucci is a professor of Probability and Mathematical Statistics at the Alma Mater Studiorum – University of Bologna. His research activity encompasses various aspects of the theory of stochastic differential equations for diffusions and jump processes, degenerate partial differential equations, and their applications to mathematical finance. He has authored 6 books and over 80 scientific articles on the following topics: linear and nonlinear Kolmogorov-Fokker-Planck equations; regularity and asymptotic estimates of transition densities for multidimensional diffusions and jump processes; free boundary problems, optimal stopping, and applications to American-style financial derivatives; Asian options and volatility models. He has been invited as a speaker at more than 40 international conferences. He serves as an editor for the Journal of Computational Finance and is the director of a postgraduate program in Mathematical Finance at the University of Bologna.
Bibliographic Information
Book Title: Probability Theory I
Book Subtitle: Random Variables and Distributions
Authors: Andrea Pascucci
Series Title: UNITEXT
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2025
Softcover ISBN: 978-3-031-63189-4Due: 20 October 2024
eBook ISBN: 978-3-031-63190-0Due: 20 October 2024
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Illustrations: 13 b/w illustrations, 16 illustrations in colour
Additional Information: Translation from the Italian language edition: “Teoria della Probabilità. Variabili aleatorie e distribuzioni” by Andrea Pascucci, © Springer-Verlag Italia S.r.l., part of Springer Nature 2020.