Markov processes, semigroups, and generators /
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Author / Creator: | Kolokolʹt︠s︡ov, V. N. (Vasiliĭ Nikitich) |
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Imprint: | Berlin ; New York : De Gruyter, ©2011. |
Description: | 1 online resource (xviii, 430 pages) : illustrations |
Language: | English |
Series: | De Gruyter studies in mathematics, 0179-0986 ; 38 De Gruyter studies in mathematics ; 38. |
Subject: | |
Format: | E-Resource Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11277653 |
Summary: | <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.</p> <p>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.</p> <p>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.</p> <p>From the contents:</p> Tools from Probability and Analysis Brownian motion Markov processes and martingales SDE, ψ 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 |
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Physical Description: | 1 online resource (xviii, 430 pages) : illustrations |
Bibliography: | Includes bibliographical references and index. |
ISBN: | 9783110250114 311025011X 3110250101 9783110250107 |
ISSN: | 0179-0986 ; |