| Markov Processes, Semigroups and Generators Contributor(s): Kolokoltsov, Vassili N. (Author) |
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ISBN: 3110250101 ISBN-13: 9783110250107 Publisher: de Gruyter OUR PRICE: $247.00 Product Type: Hardcover - Other Formats Published: March 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Mathematics | Algebra - General - Mathematics | Mathematical Analysis |
| Dewey: 519.233 |
| LCCN: 2010050783 |
| Series: de Gruyter Studies in Mathematics |
| Physical Information: 1.12" H x 6.89" W x 9.62" (1.95 lbs) 448 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 |
Contributor Bio(s): Kolokoltsov, Vassili N.: - Vassili N. Kolokoltsov, University of Warwick, UK. |