Kolokoltsov | Markov Processes, Semigroups and Generators | E-Book | sack.de
E-Book

E-Book, Englisch, Band 38, 448 Seiten

Reihe: De Gruyter Studies in Mathematics

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
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Zielgruppe


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


Autoren/Hrsg.


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


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

Vassili N. Kolokoltsov, University of Warwick, UK



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