LEADER 04787nam 22007215 450 001 9910299969203321 005 20200630042514.0 010 $a3-662-43696-5 024 7 $a10.1007/978-3-662-43696-7 035 $a(CKB)3710000000218699 035 $a(EBL)1802905 035 $a(SSID)ssj0001338851 035 $a(PQKBManifestationID)11704415 035 $a(PQKBTitleCode)TC0001338851 035 $a(PQKBWorkID)11344877 035 $a(PQKB)10674266 035 $a(MiAaPQ)EBC1802905 035 $a(DE-He213)978-3-662-43696-7 035 $a(PPN)180626922 035 $a(EXLCZ)993710000000218699 100 $a20140807d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSemigroups, Boundary Value Problems and Markov Processes /$fby Kazuaki Taira 205 $a2nd ed. 2014. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014. 215 $a1 online resource (724 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a1-322-17292-7 311 $a3-662-43695-7 320 $aIncludes bibliographical references and index. 327 $a1.Introduction and Main Results -- Part I Elements of Analysis -- 2.Elements of Probability Theory -- 3.Elements of Functional Analysis -- 4.Theory of Semigroups -- Part II Elements of Partial Differential Equations -- 5.Theory of Distributions -- 6.Sobolev and Besov Spaces -- 7.Theory of Pseudo-Differential Operators -- 8.Waldenfels Operators and Maximum Principles -- Part III Markov Processes, Semigroups and Boundary Value problems -- 9.Markov Processes, Transition Functions and Feller Semigroups -- 10.Feller Semigroups and Elliptic Boundary Value Problems -- 11.Proof of Theorem 1.3 -- 12.Markov Processes Revisited -- 13.Concluding Remarks -- Appendix: Boundedness of Pseudo-Differential Operators -- References -- Index. 330 $aA careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aFunctional analysis 606 $aHarmonic analysis 606 $aDifferential equations, Partial 606 $aProbabilities 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aFunctional analysis. 615 0$aHarmonic analysis. 615 0$aDifferential equations, Partial. 615 0$aProbabilities. 615 14$aFunctional Analysis. 615 24$aAbstract Harmonic Analysis. 615 24$aPartial Differential Equations. 615 24$aProbability Theory and Stochastic Processes. 676 $a519.233 700 $aTaira$b Kazuaki$4aut$4http://id.loc.gov/vocabulary/relators/aut$059537 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299969203321 996 $aSemigroups, boundary value problems and Markov processes$91101548 997 $aUNINA LEADER 02340oas 22009373a 450 001 9910145361503321 005 20251106213014.0 011 $a1932-9032 035 $a(OCoLC)60615802 035 $a(CONSER) 2006214572 035 $a(CKB)991042747066512 035 $a(EXLCZ)99991042747066512 100 $a20050614a19859999 sy a 101 0 $aeng 135 $aurun||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGrowth, genetics & hormones 210 $aNew York $cBiomedical Information Corp 311 08$a0898-6630 517 3 $aGrowth, genetics and hormones 606 $aHuman growth$vPeriodicals 606 $aGenetics$vPeriodicals 606 $aEndocrine System Diseases$xgenetics 606 $aGrowth 606 $aGrowth Disorders$xgenetics 606 $aGrowth Substances$xgenetics 606 $aCroissance humaine$vPe?riodiques 606 $aGe?ne?tique$vPe?riodiques 606 $aCroissance 606 $agrowth$2aat 606 $aGenetics$2fast$3(OCoLC)fst00940117 606 $aHuman growth$2fast$3(OCoLC)fst00963131 608 $aPeriodical. 608 $aPeriodicals.$2fast 608 $aPeriodicals.$2lcgft 615 0$aHuman growth 615 0$aGenetics 615 2$aEndocrine System Diseases$xgenetics. 615 2$aGrowth. 615 2$aGrowth Disorders$xgenetics. 615 2$aGrowth Substances$xgenetics. 615 6$aCroissance humaine 615 6$aGe?ne?tique 615 6$aCroissance. 615 7$agrowth. 615 7$aGenetics. 615 7$aHuman growth. 676 $a616 801 0$bOCLCS 801 1$bOCLCS 801 2$bNSD 801 2$bOCLCQ 801 2$bNSD 801 2$bOCLCQ 801 2$bHEBIS 801 2$bOCLCQ 801 2$bOCLCF 801 2$bOCLCO 801 2$bVT2 801 2$bOCLCO 801 2$bOCLCQ 801 2$bOCLCO 801 2$bOCLCQ 801 2$bOCLCO 801 2$bUAB 801 2$bOCLCQ 801 2$bREB 801 2$bOCLCO 801 2$bAU@ 801 2$bOCLCO 801 2$bOCLCQ 801 2$bOCLCO 801 2$bOCLCL 801 2$bCCO 801 2$bOCLCQ 906 $aJOURNAL 912 $a9910145361503321 996 $aGrowth, genetics & hormones$92194801 997 $aUNINA