Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / / by Kenneth Shum
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| Autore: |
Shum Kenneth
|
| Titolo: |
Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / / by Kenneth Shum
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023 |
| Edizione: | 1st ed. 2023. |
| Descrizione fisica: | 1 online resource (262 pages) |
| Disciplina: | 519.2 |
| Soggetto topico: | Probabilities |
| Measure theory | |
| Probability Theory | |
| Applied Probability | |
| Measure and Integration | |
| Teoria de la mesura | |
| Soggetto genere / forma: | Llibres electrònics |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Measure-Theoretic Probability |
| ISBN: | 3-031-49830-5 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910835058303321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Compact Textbooks in Mathematics, . 2296-455X