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
ISBN: 978-3-11-025011-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Stochastik
Weitere Infos & Material
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