Markov Processes, Semigroups and Generators / / Vassili N. Kolokoltsov.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Kolokoltsov, Vassili N.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2011
• Year of Publication: 2011
• Language: English
• Series: De Gruyter Studies in Mathematics , 38
• Physical Description: 1 online resource (430 p.)

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

Table of Contents

Frontmatter -- Preface -- Notations -- Standard abbreviations -- Contents -- I Introduction to stochastic analysis -- 1 Tools from probability and analysis -- 2 Brownian motion (BM) -- 3 Markov processes and martingales -- 4 SDE, ΨDE and martingale problems -- II Markov processes and beyond -- 5 Processes in Euclidean spaces -- 6 Processes in domains with a boundary -- 7 Heat kernels for stable-like processes -- 8 CTRW and fractional dynamics -- 9 Complex Markov chains and Feynman integral -- Bibliography -- Index