LEADER 03921nam 2200805 a 450 001 9910828220403321 005 20200520144314.0 010 $a1-283-16633-X 010 $a9786613166333 010 $a3-11-025011-X 024 7 $a10.1515/9783110250114 035 $a(CKB)2670000000088777 035 $a(EBL)690653 035 $a(OCoLC)723945552 035 $a(SSID)ssj0000530389 035 $a(PQKBManifestationID)11335404 035 $a(PQKBTitleCode)TC0000530389 035 $a(PQKBWorkID)10561630 035 $a(PQKB)11246017 035 $a(MiAaPQ)EBC690653 035 $a(DE-B1597)122967 035 $a(OCoLC)1002222248 035 $a(OCoLC)1004866909 035 $a(OCoLC)1011438942 035 $a(OCoLC)754713599 035 $a(OCoLC)979906337 035 $a(OCoLC)987921673 035 $a(OCoLC)992492806 035 $a(OCoLC)999354825 035 $a(DE-B1597)9783110250114 035 $a(Au-PeEL)EBL690653 035 $a(CaPaEBR)ebr10486491 035 $a(CaONFJC)MIL316633 035 $a(PPN)175552088 035 $a(EXLCZ)992670000000088777 100 $a20110104d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMarkov processes, semigroups, and generators$b[electronic resource] /$fVassili N. Kolokoltsov 210 $aBerlin ;$aNew York $cDe Gruyter$dc2011 215 $a1 online resource (448 p.) 225 1 $aDe Gruyter studies in mathematics,$x0179-0986 ;$v38 300 $aDescription based upon print version of record. 311 $a3-11-025010-1 320 $aIncludes bibliographical references and index. 327 $apt. 1. Introduction to stochastic analysis -- pt. 2. Markov processes and beyond. 330 $aMarkov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space. This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools. The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes. From the contents: Tools from Probability and Analysis Brownian motion Markov processes and martingales SDE, ?DE and martingale problems Processes in Euclidean spaces Processes in domains with a boundary Heat kernels for stable-like processes Continuous-time random walks and fractional dynamics Complex chains and Feynman integral 410 0$aDe Gruyter studies in mathematics ;$v38. 606 $aMarkov processes 606 $aSemigroups 606 $aGroup theory$xGenerators 610 $aGenerators. 610 $aMarkov Processes. 610 $aSemigroups. 615 0$aMarkov processes. 615 0$aSemigroups. 615 0$aGroup theory$xGenerators. 676 $a519.2/33 686 $aSK 820$2rvk 700 $aKolokol?t?sov$b V. N$g(Vasilii? Nikitich)$0441084 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910828220403321 996 $aMarkov processes, semigroups and generators$9856079 997 $aUNINA