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Home > Mathematics and Science Textbooks > Mathematics > Probability and statistics > Elementare Wahrscheinlichkeitstheorie I: Zufallsvariablen and Verteilungen
Elementare Wahrscheinlichkeitstheorie I: Zufallsvariablen and Verteilungen

Elementare Wahrscheinlichkeitstheorie I: Zufallsvariablen and Verteilungen


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About the Book

Dieses Buch bietet eine prägnante und zugleich rigorose Einführung in die Wahrscheinlichkeitstheorie. Aus den möglichen Zugängen zum Thema wurde der modernste Ansatz auf Grundlage der Maßtheorie gewählt: Dieser Ansatz erfordert ein höheres Maß an mathematischer Abstraktion und Komplexität, ist jedoch unerlässlich, um fortgeschrittene Themen wie Stochastische Prozesse, Stochastische Differentialrechnung und Statistische Inferenz zu verstehen. Der vorliegende Text resultiert aus den Erfahrungen, die im Rahmen von Kursen für Wahrscheinlichkeitstheorie und angewandte Mathematik im Mathematikstudium an der Universität Bologna gewonnen wurden. Dieses Buch richtet sich an Studierende im zweiten oder dritten Jahr ihres Studiums in Mathematik, Physik oder einer anderen Naturwissenschaft und setzt Kenntnisse mehrdimensionaler Differential- und Integralrechnung voraus. Die vier Kapitel behandeln folgende Themen: Maße und Wahrscheinlichkeitsräume, Zufallsvariablen, Folgen von Zufallsvariablen und Grenzwertsätze, Erwartungswert und bedingte Verteilung. Außerdem beinhaltet dieses Buch eine umfangreiche Sammlung gelöster Übungen.

Table of Contents:
1 Maße und Wahrscheinlichkeitsräume.- 2 Zufallsvariablen.- 3 Folgen von Zufallsvariablen.- 4 Bedingte Wahrscheinlichkeit.- Anhang A: Dynkins Theoreme.- Anhang B: Absolute Stetigkeit.- Anhang C: Gleichgradige Integrierbarkeit.

About the Author :
Andrea Pascucci ist Professor für Wahrscheinlichkeitstheorie und mathematische Statistik an der Alma Mater Studiorum - Universität Bologna. Seine Forschungsaktivitäten umfassen verschiedene Aspekte der Theorie stochastischer Differentialgleichungen für Diffusions- und Sprungprozesse, degenerierte partielle Differentialgleichungen und deren Anwendungen in der mathematischen Finanzwirtschaft. Er hat sechs Bücher und über 80 wissenschaftliche Artikel zu folgenden Themen verfasst: lineare und nichtlineare Kolmogorov-Fokker-Planck-Gleichungen; Regularität und asymptotische Abschätzungen von Übergangsdichten für mehrdimensionale Diffusions- und Sprungprozesse; Freie Randwertprobleme, optimale Stopp-Probleme und Anwendungen auf amerikanische Finanzderivate; Asiatische Optionen und Volatilitätsmodelle. Er wurde als Referent zu mehr als 40 internationalen Konferenzen eingeladen. Er ist Herausgeber des Journal of Computational Finance und Leiter eines Postgraduierten-Programms für Mathematische Finanzwirtschaft an der Universität Bologna.


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Product Details
  • ISBN-13: 9783031980923
  • Publisher: Springer International Publishing AG
  • Publisher Imprint: Springer Spektrum
  • Height: 235 mm
  • No of Pages: 290
  • Sub Title: Zufallsvariablen and Verteilungen
  • ISBN-10: 3031980921
  • Publisher Date: 28 Dec 2025
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Width: 155 mm


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Elementare Wahrscheinlichkeitstheorie I: Zufallsvariablen and Verteilungen
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