From Brownian Motion to Schrödinger’s Equation

1995
ISBN: 978-3-540-57030-1
Verlag: Springer

Buch, Englisch, Band 312, 292 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 643 g

Reihe: Grundlehren der mathematischen Wissenschaften

In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics.
A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature.

Zielgruppe

Research

Autoren/Hrsg.

Chung, Kai L.

Zhao, Zhongxin

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik

Inhaltsverzeichnis

1. Preparatory Material.- 2. Killed Brownian Motion.- 3. Schrödinger Operator.- 4. Stopped Feynman-Kac Functional.- 5. Conditional Brownian Motion and Conditional Gauge.- 6. Green Functions.- 7. Conditional Gauge and q-Green function.- 8. Various Related Developments.- 9. The Case of One Dimension.- References.