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Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / by Kenneth Shum.
Springer Nature - Springer Mathematics and Statistics eBooks 2023 English International Available online
View online- Format:
- Book
- Author/Creator:
- Shum, Kenneth.
- Series:
- Compact Textbooks in Mathematics, 2296-455X
- Language:
- English
- Subjects (All):
- Probabilities.
- Measure theory.
- Probability Theory.
- Applied Probability.
- Measure and Integration.
- Local Subjects:
- Probability Theory.
- Applied Probability.
- Measure and Integration.
- Physical Description:
- 1 online resource (262 pages)
- Edition:
- 1st ed. 2023.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Birkhäuser, 2023.
- Summary:
- 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 necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector’s problem, Monte Carlo integration in finance, data compression in information theory, and more. Measure-Theoretic Probability is ideal for a one-semester course and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study. Prerequisites include a basic knowledge of probability and elementary concepts from real analysis.
- Contents:
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-031-49830-5
- OCLC:
- 1424745713
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