| Description |
1 online resource (xviii, 430 pages) : illustrations |
| Series |
De Gruyter studies in mathematics, 0179-0986 ; 38 |
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De Gruyter studies in mathematics ; 38. 0179-0986
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| Contents |
880-01 pt. 1. Introduction to stochastic analysis -- pt. 2. Markov processes and beyond |
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880-01/(S 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 |
| Summary |
880-02 This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for applications. This work does just that, and with the necessary mathematical rigor |
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880-02/(S 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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
In English |
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Print version record |
| Subject |
Markov processes.
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Semigroups.
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Group theory -- Generators.
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MATHEMATICS -- Probability & Statistics -- Stochastic Processes.
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Group theory -- Generators
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Markov processes
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Semigroups
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Markov-Prozess
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| Form |
Electronic book
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| LC no. |
2010050783 |
| ISBN |
9783110250114 |
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311025011X |
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3110250101 |
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9783110250107 |
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