Vassili N. Kolokoltsov

Markov Processes, Semigroups and Generators

• Gebundenes Buch

Produktbeschreibung

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-semestercourse 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

Produktdetails

• De Gruyter Studies in Mathematics 38
• Verlag: De Gruyter
• Seitenzahl: 448
• Erscheinungstermin: 17. März 2011
• Englisch
• Abmessung: 246mm x 175mm x 30mm
• Gewicht: 886g
• ISBN-13: 9783110250107
• ISBN-10: 3110250101
• Artikelnr.: 33559678

Autorenporträt

Vassili N. Kolokoltsov, University of Warwick, UK.

Inhaltsangabe

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.

Rezensionen

"[...] 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