Continuous Strong Markov Processes in Dimension One

A Stochastic Calculus Approach
1998
ISBN: 978-3-540-64465-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 140 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 242 g

Reihe: Lecture Notes in Mathematics

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Zielgruppe

Research

Autoren/Hrsg.

Schmidt, Wolfgang M.

Assing, Sigurd

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Basic concepts and preparatory results.- Classification of the points of the state space.- Weakly additive functionals and time change of strong Markov processes.- Semimartingale decomposition of continuous strong Markov semimartingales.- Occupation time formula.- Construction of continuous strong Markov processes.- Continuous strong Markov semimartingales as solutions of stochastic differential equations.