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, Levy 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

About the Author

Vassili N. Kolokoltsov, University of Warwick, UK.

Book Information
ISBN 9783110250107
Author Vassili N. Kolokoltsov
Format Hardback
Page Count 448
Imprint De Gruyter
Publisher De Gruyter
Weight(grams) 886g