03921nam 2200805 a 450 991078999900332120200520144314.01-283-16633-X97866131663333-11-025011-X10.1515/9783110250114(CKB)2670000000088777(EBL)690653(OCoLC)723945552(SSID)ssj0000530389(PQKBManifestationID)11335404(PQKBTitleCode)TC0000530389(PQKBWorkID)10561630(PQKB)11246017(MiAaPQ)EBC690653(DE-B1597)122967(OCoLC)1002222248(OCoLC)1004866909(OCoLC)1011438942(OCoLC)754713599(OCoLC)979906337(OCoLC)987921673(OCoLC)992492806(OCoLC)999354825(DE-B1597)9783110250114(Au-PeEL)EBL690653(CaPaEBR)ebr10486491(CaONFJC)MIL316633(PPN)175552088(EXLCZ)99267000000008877720110104d2011 uy 0engur|n|---|||||txtccrMarkov processes, semigroups, and generators[electronic resource] /Vassili N. KolokoltsovBerlin ;New York De Gruyterc20111 online resource (448 p.)De Gruyter studies in mathematics,0179-0986 ;38Description based upon print version of record.3-11-025010-1 Includes bibliographical references and index.pt. 1. Introduction to stochastic analysis -- pt. 2. Markov processes and beyond.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 De Gruyter studies in mathematics ;38.Markov processesSemigroupsGroup theoryGeneratorsGenerators.Markov Processes.Semigroups.Markov processes.Semigroups.Group theoryGenerators.519.2/33SK 820rvkKolokolʹt͡sov V. N(Vasiliĭ Nikitich)441084MiAaPQMiAaPQMiAaPQBOOK9910789999003321Markov processes, semigroups and generators856079UNINA