Probability theory: 1 Random variables and distributions
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 provid...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2024]
|
| Schriftenreihe: | Unitext - Matematica per il 3 + 2
Volume 165 |
| Schlagwörter: | |
| Zusammenfassung: | 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 |
| Beschreibung: | 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. |
| Umfang: | xxi, 382 Seiten Illustrationen |
| ISBN: | 9783031631894 |
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| 500 | |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. | ||
| 520 | |a 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 | ||
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| id | DE-604.BV050126944 |
| illustrated | Illustrated |
| indexdate | 2025-02-10T13:10:56Z |
| institution | BVB |
| isbn | 9783031631894 |
| language | English |
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| physical | xxi, 382 Seiten Illustrationen |
| publishDate | 2024 |
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| series | Unitext - Matematica per il 3 + 2 |
| series2 | Unitext - Matematica per il 3 + 2 |
| spelling | Pascucci, Andrea 1969- Verfasser (DE-588)110031573X aut Probability theory 1 Random variables and distributions Andrea Pascucci Cham, Switzerland Springer [2024] xxi, 382 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Unitext - Matematica per il 3 + 2 Volume 165 Unitext - Matematica per il 3 + 2 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 Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Verteilung (DE-588)4432264-1 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Zufallsvariable (DE-588)4129514-6 s Verteilung (DE-588)4432264-1 s DE-604 (DE-604)BV050126922 1 Erscheint auch als Online-Ausgabe 978-3-031-63190-0 Unitext - Matematica per il 3 + 2 Volume 165 (DE-604)BV047304938 165 |
| spellingShingle | Pascucci, Andrea 1969- Probability theory Unitext - Matematica per il 3 + 2 Zufallsvariable (DE-588)4129514-6 gnd Verteilung (DE-588)4432264-1 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4129514-6 (DE-588)4432264-1 (DE-588)4079013-7 |
| title | Probability theory |
| title_auth | Probability theory |
| title_exact_search | Probability theory |
| title_full | Probability theory 1 Random variables and distributions Andrea Pascucci |
| title_fullStr | Probability theory 1 Random variables and distributions Andrea Pascucci |
| title_full_unstemmed | Probability theory 1 Random variables and distributions Andrea Pascucci |
| title_short | Probability theory |
| title_sort | probability theory random variables and distributions |
| topic | Zufallsvariable (DE-588)4129514-6 gnd Verteilung (DE-588)4432264-1 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Zufallsvariable Verteilung Wahrscheinlichkeitstheorie |
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