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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
Law Of Large Numbers Central Limit Theorem Large Deviations Convergence Of Random Variables |
| 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. S-algebras 2. Measures 3. Equality of finite measures 4. Description of probability measures 5. Measurable functions 6. Integration 7. Random variable distribution and integration 8. Ways of convergence of random variables 9. Product measures 10. Independence 11. Borel-Cantelli entries and Kolmogorov's 0-1 law 12. The strong law of large numbers 13. Characteristic functions 14. Convergence by distribution 15. Convergence by distribution and characteristic functions 16. The central limit theorem 17. Large deviations |
| Number of pages |
158 |
| Publication Origin: |
Kallipos, Open Academic Editions |
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