Probability Theory I

Random Variables and Distributions

AvAndrea Pascucci

Häftad, Engelska, 2024

Del 165 i serien UNITEXT

641 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2024-10-19
Mått:155 x 235 x 21 mm
Vikt:684 g
Format:Häftad
Språk:Engelska
Serie:UNITEXT
Antal sidor:382
Förlag:Springer International Publishing AG
ISBN:9783031631894
Originaltitel:Teoria della Probabilità. Variabili aleatorie e distribuzioni

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Mer om författaren

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.

Innehållsförteckning

1 Measures and probability spaces.- 2 Random variables.- 3 Sequences of random variables.- 4 Conditional probability.- 5 Summary exercises.- Appendix A: Dynkin’s theorems.- Appencix B: Absolute continuity.- Appendix C: Uniform integrability.