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Markov Processes, Semigroups and Generators

Markov Processes, Semigroups and Generators by Vassili N. Kolokoltsov
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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
De Gruyter; March 2011
448 pages; ISBN 9783110250114
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Title: Markov Processes, Semigroups and Generators
Author: Vassili N. Kolokoltsov
 
Subject categories
ISBNs
311025011X
9783110250107
9783110250114