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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik An Introduction to the Modern Martingale Theory and Applications
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An Introduction to the Modern Martingale Theory and Applications
Wilfredo Urbina-Romero, Ricardo Rios (Gebundene Ausgabe, Englisch)
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Beschreibung
Martingale theory is a cornerstone of modern probability, offering a natural extension of the study of sums of independent random variables. Although its roots can be traced back to the work of Paul Lévy in 1937, it was Joseph L. Doob in the 1940s who formally developed the theory, culminating in his landmark book Stochastic Processes in 1953. Since then, martingale theory has evolved… significantly, with deep contributions from mathematicians such as Donald L. Burkholder, Richard Gundy, and Burgess Davis, among others. This is what is now known as advanced martingale theory, which began with the publication of Burkholder’s seminal paper Martingale Transforms in 1966. This book provides a comprehensive treatment of both classical and advanced martingale theory. It opens with a historical introduction, exploring foundational functions such as Rademacher, Haar, and Walsh functions, before delving into the core concepts of conditional probability. The classical theory, as developed by Doob, is meticulously presented, followed by an in-depth examination of modern advancements, including Burkholder’s inequalities, Burkholder-Davis-Gundy inequality, and their generalizations, as well as good-lambda inequalities. The final chapter showcases a wide range of applications, highlighting the theory’s profound impact on Banach space theory, harmonic analysis, and beyond. Intended for graduate students and researchers in probability and analysis, this book serves as both an introduction and a reference, offering a clear and structured approach to a subject that continues to shape mathematical research and its applications. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
02.10.2025
Sprache
Englisch
EAN
9783031889028
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Texts in Applied Mathematics
Sonderedition
Nein
Autor
Wilfredo Urbina-Romero, Ricardo Rios
Seitenanzahl
276
Einbandart
Gebundene Ausgabe
Buch Untertitel
An Analytic View
Schlagwörter
martingale with discrete parameter, martingale transforms, good lambda inequalities, Burkholder-Davis-Gundy inequalities, Haar and Walsh systems, martingale limit theorems, operators on martingales, martingales and geometry in Banach spaces
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Birkhäuser, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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