Concentration and Gaussian Approximation for Randomized Sums
This book describes extensions of Sudakov's classical result on the concentration of measure phenomenon for weighted sums of dependent random variables. The central topics of the book are weighted sums of random variables and the concentration of their distributions around Gaussian laws. The an...
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| Main Authors: | , , |
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| Korporativna značnica: | |
| Format: | Elektronski eKnjiga |
| Jezik: | angleščina |
| Izdano: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2023.
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| Izdaja: | 1st ed. 2023. |
| Serija: | Probability Theory and Stochastic Modelling,
104 |
| Teme: | |
| Online dostop: | https://doi.org/10.1007/978-3-031-31149-9 |
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Kazalo:
- Part I. Generalities
- 1. Moments and correlation conditions
- 2. Some classes of probability distributions
- 3. Characteristic functions
- 4. Sums of independent random variables
- Part II. Selected topics on concentration
- 5. Standard analytic conditions
- 6. Poincaré-type inequalities
- 7. Logarithmic Sobolev inequalities
- 8. Supremum and infimum convolutions
- Part IV. Analysis on the sphere
- 9. Sobolev-type inequalities
- 10. Second order spherical concentration
- 11. Linear functionals on the sphere
- Part V. First applications to randomized sums
- 12. Typical distributions
- 13. Characteristic functions of weighted sums
- 14. Fluctuations of distributions
- Part VI. Refined bounds and rates
- 15. L^2 expansions and estimates
- 16. Refinements for the Kolmogorov distance
- 17. Applications of the second order correlation condition
- Part VII. Distributions and coefficients of special types
- 18. Special systems and examples
- 19. Distributions with symmetries
- 20. Productmeasures
- 21. Coefficients of Special type
- Glossary.