Markov Processes, Semigroups and Generators

Buch | Hardcover
XVIII, 430 Seiten
2011
De Gruyter (Verlag)
978-3-11-025010-7 (ISBN)

Lese- und Medienproben

Markov Processes, Semigroups and Generators - Vassili N. Kolokoltsov
179,95 inkl. MwSt
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
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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