000 03456nam a22005055i 4500
001 978-88-7642-499-1
003 DE-He213
005 20160302173521.0
007 cr nn 008mamaa
008 140701s2014 it | s |||| 0|eng d
020 _a9788876424991
_9978-88-7642-499-1
024 7 _a10.1007/978-88-7642-499-1
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aPrato, Giuseppe Da.
_eauthor.
245 1 0 _aIntroduction to Stochastic Analysis and Malliavin Calculus
_h[electronic resource] /
_cby Giuseppe Da Prato.
264 1 _aPisa :
_bScuola Normale Superiore :
_bImprint: Edizioni della Normale,
_c2014.
300 _aXVII, 279 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aPublications of the Scuola Normale Superiore ;
_v13
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aMeasure theory.
650 0 _aProbabilities.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aFunctional Analysis.
650 2 4 _aMeasure and Integration.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9788876424977
830 0 _aPublications of the Scuola Normale Superiore ;
_v13
856 4 0 _uhttp://dx.doi.org/10.1007/978-88-7642-499-1
912 _aZDB-2-SMA
999 _c212361
_d212361