Measure-Theoretic Probability With Applications to Statistics, Finance, and Engineering /
This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not n...
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| Autor corporatiu: | |
| Format: | Electrònic eBook |
| Idioma: | anglès |
| Publicat: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2023.
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| Edició: | 1st ed. 2023. |
| Col·lecció: | Compact Textbooks in Mathematics,
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| Matèries: | |
| Accés en línia: | https://doi.org/10.1007/978-3-031-49830-5 |
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Taula de continguts:
- Preface
- Beyond discrete and continuous random variables
- Probability spaces
- Lebesgue–Stieltjes measures
- Measurable functions and random variables
- Statistical independence
- Lebesgue integral and mathematical expectation
- Properties of Lebesgue integral and convergence theorems
- Product space and coupling
- Moment generating functions and characteristic functions
- Modes of convergence
- Laws of large numbers
- Techniques from Hilbert space theory
- Conditional expectation
- Levy’s continuity theorem and central limit theorem
- References
- Index.