Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / by Kenneth Shum

Von:

Shum, Kenneth [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Compact Textbooks in MathematicsVerlag: Cham : Springer International Publishing, 2023Verlag: Cham : Imprint: Birkhäuser, 2023Auflage: 1st ed. 2023Beschreibung: 1 Online-Ressource(XV, 259 p. 33 illus., 25 illus. in color.)ISBN:

9783031498305

Schlagwörter:

Andere physische Formen: 9783031498299 | 9783031498312 | 9783031498329 | Erscheint auch als: 9783031498299 Druck-Ausgabe | Erscheint auch als: 9783031498312 Druck-Ausgabe | Erscheint auch als: 9783031498329 Druck-AusgabeDOI: DOI: 10.1007/978-3-031-49830-5Online-Ressourcen:

Zugang im Netz des KIT

Zusammenfassung: 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.Zusammenfassung: 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.PPN: PPN: 1881223558Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

Exemplare ( 0 )

Dieser Titel hat keine Exemplare