Markov Processes, Semigroups and Generators / / Vassili N. Kolokoltsov.
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 scienc...
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Superior document: | Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2011] ©2011 |
Year of Publication: | 2011 |
Language: | English |
Series: | De Gruyter Studies in Mathematics ,
38 |
Online Access: | |
Physical Description: | 1 online resource (430 p.) |
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Other title: | 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 |
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Summary: | 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 |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110250114 9783110494938 9783110238570 9783110238471 9783110637205 9783110261189 9783110261233 9783110261202 |
ISSN: | 0179-0986 ; |
DOI: | 10.1515/9783110250114 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Vassili N. Kolokoltsov. |