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Title Details:
A second lesson in probabilities
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.
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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