Kolokoltsov Markov Processes, Semigroups and Generators

1. Auflage 2011
ISBN: 978-3-11-025011-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 38, 448 Seiten

Reihe: De Gruyter Studies in Mathematics

Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space.

This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools.

The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes.

From the contents:

• Tools from Probability and Analysis
• Brownian motion
• Markov processes and martingales
• SDE, ?DE and martingale problems
• Processes in Euclidean spaces
• Processes in domains with a boundary
• Heat kernels for stable-like processes
• Continuous-time random walks and fractional dynamics
• Complex chains and Feynman integral

Zielgruppe

Mathematicians, Mathematical Physicists, Biologists and Sociologists Involved in Research on Random Processes, Advanced Students; Academic Libraries

Autoren/Hrsg.

Kolokoltsov, Vassili N.

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Frontmatter
Preface
Notations
Standard abbreviations
Contents
I Introduction to stochastic analysis
1 Tools from probability and analysis
2 Brownian motion (BM)
3 Markov processes and martingales
4 SDE, ?DE and martingale problems
II Markov processes and beyond
5 Processes in Euclidean spaces
6 Processes in domains with a boundary
7 Heat kernels for stable-like processes
8 CTRW and fractional dynamics
9 Complex Markov chains and Feynman integral
Bibliography
Index

Über Autor(innen)

Kolokoltsov, Vassili N.
Vassili N. Kolokoltsov, University of Warwick, UK