Markov Processes, Semigroups and Generators

von Vassili N. Kolokoltsov

430 Seiten, Hardcover

Kurzbeschreibung des Verlags

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

• Reihe: De Gruyter Studies in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Angewandte Mathematik Stochastik
• ISBN: 9783110250107
• Sprache: Englisch
• Erscheinungsdatum: 17.03.2011
• Größe: 24 x 17 cm
• Verlag: De Gruyter