01684nam a2200169   4500020001800000041001200018082002000030084002500050100002100075245006300096250000600159260002900165300001000194500104100204505023501245650003401480  a9783031631894  aEnglish  a330.0212bPAS/P  2Colon Classification  aPascucci, Andrea  aProbability Theory I :bRandom Variables and Distributions  a1  aItaly:bSpringer,c2024.  a382p.  aThis 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.  a
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
  aEconomics- Probability Theory