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OverviewMarkov 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 Full Product DetailsAuthor: Vassili N. Kolokoltsov , Vassili N KolokoltsovPublisher: De Gruyter Imprint: De Gruyter Volume: 38 Dimensions: Width: 17.00cm , Height: 2.80cm , Length: 24.00cm Weight: 0.886kg ISBN: 9783110250107ISBN 10: 3110250101 Pages: 448 Publication Date: 17 March 2011 Recommended Age: College Graduate Student Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPart I Brownian Motion, Markov Processes, Martingales. 1 Preliminaries in Probability and Analysis. 2 Browninan Motion I: Constructions. 3 Martingales and Markov Processes. 4 Browninan Motion II: Elements of Analysis. Part II Basic Constructions of Markov Semigroups. 1 Analytic Constructions. 2 Probabilistic Constructions. 3 Heat Kernel Estimates. 4 Process in Cones and Bounded Domains. Part III Extensions, Developments, Applications. 1 CTRW and Fractional Dynamics. 2 Complex Markov Chains and Feynman integral. 3 Controlled Processes. 4 Semiclassical Asymptotic. 5 Miscellany. 6 Bibliographical Comments.Reviews[...] As a whole, the book is a valuable source of information both for specialists in the field and those who study the theory of stochastic processes. Anatoly N. Kochubei, Zentralblatt fur Mathematik [...] As a whole, the book is a valuable source of information both for specialists in the field and those who study the theory of stochastic processes. Anatoly N. Kochubei, Zentralblatt fr Mathematik [...] As a whole, the book is a valuable source of information both for specialists in the field and those who study the theory of stochastic processes. Anatoly N. Kochubei, Zentralblatt f�r Mathematik [...] As a whole, the book is a valuable source of information both for specialists in the field and those who study the theory of stochastic processes. Anatoly N. Kochubei, Zentralblatt fur Mathematik Author InformationVassili N. Kolokoltsov, University of Warwick, UK. Tab Content 6Author Website:Countries AvailableAll regions |
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