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| Title Details: | |
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A second lesson in probabilities |
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| Authors: |
Cheliotis, Dimitrios |
| Reviewer: |
Loulakis, Michail |
| Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES > FOUNDATIONS OF PROBABILITY THEORY MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES > LIMIT THEOREMS |
| Keywords: |
Probability Measures
Convergence Of Random Variables Law Of Large Numbers Central Limit Theorem Large Deviations |
| Description: | |
| Abstract: |
The aims of the book are twofold. First to expose the basic terminology of metric probability theory, and then to study the marginal behavior of sequences of random variables. The two main types of convergence in probability theory, almost certain and distributional convergence, are covered. The basic technique for proving results for each of them is presented, and applied to the proof of the strong law of large numbers and the central limit theorem. Finally, an introduction to the theory of large deviations is given.
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| Linguistic Editors: |
Trampoulis, Τheofilos |
| Type: |
Undergraduate textbook |
| Creation Date: | 2015 |
| Item Details: | |
| ISBN |
978-960-603-296-7 |
| License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
| DOI | http://dx.doi.org/10.57713/kallipos-744 |
| Handle | http://hdl.handle.net/11419/2825 |
| Bibliographic Reference: | Cheliotis, D. (2015). A second lesson in probabilities [Undergraduate textbook]. Kallipos, Open Academic Editions. https://dx.doi.org/10.57713/kallipos-744 |
| Language: |
Greek |
| Consists of: |
1. Σ-άλγεβρες 2. Μέτρα 3. Ισότητα πεπερασμένων μέτρων 4. Κατασκευή μέτρων πιθανότητας 5. Μετρήσιμες συναρτήσεις 6. Ολοκλήρωση 7. Σύγκλιση τυχαίων μεταβλητών 8. Ανεξαρτησία 9. Τα λήμματα Borel-Cantelli και ο νόμος 0-1 του Kolmogorov 10. Ο ισχυρός νόμος των μεγάλων αριθμών 11. Χαρακτηριστικές συναρτήσεις 12. Σύγκλιση κατά κατανομή 13. Σύγκλιση κατά κατανομή και χαρακτηριστικές συναρτήσεις 14. Το κεντρικό οριακό θεώρημα 15. Μεγάλες αποκλίσεις 16. Κατανομή τυχαίας μεταβλητής και ολοκλήρωση 17. Μέτρα γινόμενο |
| Number of pages |
158 |
| Publication Origin: |
Kallipos, Open Academic Editions |
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