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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Measure, Probability and Functional Analysis
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Measure, Probability and Functional Analysis
Hannah Geiss, Stefan Geiss (Broschiert, Englisch)
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Beschreibung
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 introduction to measure theory, with a special focus on probability spaces. Next, Lebesgue integration… theory is developed in full detail covering the main methods and statements, followed by the important limit theorems of probability. Advanced limit theorems, such as the Berry-Esseen Theorem and Stein’s method, are included. The final part of the book explores interactions between probability and functional analysis. It includes an introduction to Banach function spaces, such as Lorentz and Orlicz spaces, and to random variables with values in Banach spaces. The Itô–Nisio Theorem, the Strong Law of Large Numbers in Banach spaces, and the Bochner, Pettis, and Dunford integrals are presented. As an application, Brownian motion is rigorously constructed and investigated using Banach function space methods. Based on courses taught by the authors, this book can serve as the main text for a graduate-level course on probability, and each chapter contains a collection of exercises. The unique combination of probability and functional analysis, as well as the advanced and original topics included, will also appeal to researchers working in probability and related fields. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.03.2025
Sprache
Englisch
EAN
9783031840661
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Universitext
Sonderedition
Nein
Autor
Hannah Geiss, Stefan Geiss
Seitenanzahl
443
Einbandart
Broschiert
Schlagwörter
Probability Theory, Measure Spaces, Random Variables and their Convergence, Lebesgue Integral, Uniform Integrability, Vitali's Convergence Theorem, Independence, Strong Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Berry-Esseen Theorem, Radon-Nikodym Theorem, Stein's Method, Bochner-Khinchin Theorem, Conditional Expectation, Kolmogorov Zero-One Law and Ergodicity, Weak Convergence, Fourier Transform of a Measure, Characteristic Function of a Random Variable, Theorem of Caratheodory
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
PBKF - Funktionalanalysis und Abwandlungen
PBKL - Integralrechnung und -gleichungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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