LEADER 04558nam 22007215 450 001 9910299978903321 005 20200701080229.0 010 $a88-7642-499-7 024 7 $a10.1007/978-88-7642-499-1 035 $a(CKB)3710000000212215 035 $a(Springer)9788876424991 035 $a(MH)014131722-1 035 $a(SSID)ssj0001297264 035 $a(PQKBManifestationID)11843852 035 $a(PQKBTitleCode)TC0001297264 035 $a(PQKBWorkID)11362968 035 $a(PQKB)11114779 035 $a(DE-He213)978-88-7642-499-1 035 $a(MiAaPQ)EBC6311193 035 $a(MiAaPQ)EBC5579017 035 $a(Au-PeEL)EBL5579017 035 $a(OCoLC)892541717 035 $a(PPN)179923870 035 $a(EXLCZ)993710000000212215 100 $a20140701d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to Stochastic Analysis and Malliavin Calculus /$fby Giuseppe Da Prato 205 $a1st ed. 2014. 210 1$aPisa :$cScuola Normale Superiore :$cImprint: Edizioni della Normale,$d2014. 215 $a1 online resource (XVII, 279 p.)$conline resource 225 1 $aLecture Notes (Scuola Normale Superiore) ;$v13 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a88-7642-497-0 320 $aIncludes bibliographical references. 327 $aIntroduction -- 1 Gaussian measures in Hilbert spaces -- 2 Gaussian random variables -- 3 The Malliavin derivative -- 4 Brownian Motion -- 5 Markov property of Brownian motion -- 6 Ito?s integral -- 7 Ito?s formula -- 8 Stochastic differential equations -- 9 Relationship between stochastic and parabolic equations -- 10 Formulae of Feynman?Kac and Girsanov -- 11 Malliavin calculus -- 12 Asymptotic behaviour of transition semigroups -- A The Dynkin Theorem -- B Conditional expectation -- C Martingales -- D Fixed points depending on parameters -- E A basic ergodic theorem -- References. 330 $aThis volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devoted to the differentiability of the Feynman-Kac semigroup is introduced. A considerable number of corrections and improvements have been made. 410 0$aLecture Notes (Scuola Normale Superiore) ;$v13 606 $aProbabilities 606 $aFunctional analysis 606 $aMeasure theory 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 615 0$aProbabilities. 615 0$aFunctional analysis. 615 0$aMeasure theory. 615 14$aProbability Theory and Stochastic Processes. 615 24$aFunctional Analysis. 615 24$aMeasure and Integration. 676 $a519.2 700 $aDa Prato$b Giuseppe$4aut$4http://id.loc.gov/vocabulary/relators/aut$0314271 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299978903321 996 $aIntroduction to stochastic analysis and Malliavin calculus$9251527 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress