03515nam a22006015i 4500 978-3-031-63190-0 DE-He213 20251030113234.0 cr nn 008mamaa 241019s2024 sz | s |||| 0|eng d 9783031631900 978-3-031-63190-0 10.1007/978-3-031-63190-0 doi QA274-274.9 PBT bicssc PBWL bicssc MAT029040 bisacsh PBT thema PBWL thema Pascucci, Andrea. author. (orcid)0000-0001-8837-5568 https://orcid.org/0000-0001-8837-5568 aut http://id.loc.gov/vocabulary/relators/aut 77738 Probability Theory I [electronic resource] : Random Variables and Distributions / by Andrea Pascucci. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XXI, 382 p. 24 illus., 16 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda La Matematica per il 3+2, 2038-5757 ; 165 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. 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. Stochastic processes. 76770 Mathematical physics. Probabilities. 65724 Econometrics. 57695 Mathematics. 65523 Stochastic Processes. 76770 Theoretical, Mathematical and Computational Physics. 65563 Probability Theory. 67428 Quantitative Economics. 70330 Mathematics. 65523 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031631894 Printed edition: 9783031631917 La Matematica per il 3+2, 2038-5757 ; 165 70145 https://doi.org/10.1007/978-3-031-63190-0 ZDB-2-SMA ZDB-2-SXMS 64309 64309