Markov Processes, Semigroups and Generators
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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, ψDE 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
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, ψDE 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
Vassili N. Kolokoltsov, University of Warwick, UK.
Part I Brownian Motion, Markov Processes, Martingales.
1 Preliminaries in Probability and Analysis.
2 Browninan Motion I: Constructions.
3 Martingales and Markov Processes.
4 Browninan Motion II: Elements of Analysis.
Part II Basic Constructions of Markov Semigroups.
1 Analytic Constructions.
2 Probabilistic Constructions.
3 Heat Kernel Estimates.
4 Process in Cones and Bounded Domains.
Part III Extensions, Developments, Applications.
1 CTRW and Fractional Dynamics.
2 Complex Markov Chains and Feynman integral.
3 Controlled Processes.
4 Semiclassical Asymptotic.
5 Miscellany.
6 Bibliographical Comments.
"[...] As a whole, the book is a valuable source of information both for specialists in the field and those who study the theory of stochastic processes."
Anatoly N. Kochubei, Zentralblatt für Mathematik
| Erscheint lt. Verlag | 17.3.2011 |
|---|---|
| Reihe/Serie | De Gruyter Studies in Mathematics ; 38 |
| Verlagsort | Berlin/Boston |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Gewicht | 886 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Naturwissenschaften ► Physik / Astronomie ► Thermodynamik | |
| Schlagworte | generators • Halbgruppen • Markov Processes • Markov Processes; Semigroups; Generators • Markov Processes, Semigroups, random processes • Markov-Prozesse • semigroups |
| ISBN-10 | 3-11-025010-1 / 3110250101 |
| ISBN-13 | 978-3-11-025010-7 / 9783110250107 |
| Zustand | Neuware |
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