Measure, Probability and Functional Analysis
This textbook offers a self-contained introduction to probability, covering all topics required for further study in stochastic processes and stochastic analysis, as well as some advanced topics at the interface between probability and functional analysis. The initial chapters provide a rigorous int...
I tiakina i:
| Ngā kaituhi matua: | , |
|---|---|
| Kaituhi rangatōpū: | |
| Hōputu: | Tāhiko īPukapuka |
| Reo: | Ingarihi |
| I whakaputaina: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
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| Putanga: | 1st ed. 2025. |
| Rangatū: | Universitext,
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| Ngā marau: | |
| Urunga tuihono: | https://doi.org/10.1007/978-3-031-84067-8 |
| Ngā Tūtohu: |
Tāpirihia he Tūtohu
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Rārangi ihirangi:
- - 1. Introduction – with two examples
- 2. Measure spaces and probability spaces
- 3. Construction of measure spaces
- 4. *Metric and Banach spaces
- 5. *Measures on metric spaces
- 6. Random variables and measurable maps
- 7. Independence
- 8. Integration
- 9. Convergence of random variables
- 10. The theorem of Radon-Nikodym and conditional expectation
- 11. Fourier transform and Gaussian distributions
- 12. Weak convergence
- 13. Strong law of large numbers
- 14. An ergodic theorem
- 15. Limit theorems for weak convergence
- 16. Fourier inversion formulas
- 17. Norm estimates for the Fourier transform
- 18. Riesz representation theorems
- 19. Banach function spaces
- 20. Probability in Banach spaces
- 21. Law of iterated logarithm
- 22. An application to non-life insurance.