Stochastic Processes: General Theory

1995. Auflage 1995
ISBN: 978-0-7923-3725-6
Verlag: Springer Us

Buch, Englisch, Band 342, 628 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 1315 g

Reihe: Mathematics and Its Applications

starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested.
The book is a completely revised and enlarged version of the author's (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material.
Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.

Zielgruppe

Research

Autoren/Hrsg.

Rao, Malempati M

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

I: Introduction and foundations.- II: Conditioning and martingales.- III: Stochastic function theory.- IV: Refinements in martingale analysis.- V: Martingale decompositions and integration.- VI: Stochastic integrals and differential systems.- VII: Stochastic analysis on differential structures.- Notation index.- Author index.