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Markov Processes, Semigroups and Generators
Hardcover
Series: de Gruyter Studies in Mathematics, Book 38
AlgebraGeneral MathematicsProbability & Statistics
ISBN13: 9783110250107
Publisher: De Gruyter
Published: Mar 17 2011
Pages: 448
Weight: 1.95
Height: 1.12 Width: 6.89 Depth: 9.62
Language: English
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
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