LEADER 04109nam 2200625 450 001 996466653603316 005 20230718043320.0 010 $a3-540-48161-3 024 7 $a10.1007/BFb0092416 035 $a(CKB)1000000000437297 035 $a(SSID)ssj0000326949 035 $a(PQKBManifestationID)12069034 035 $a(PQKBTitleCode)TC0000326949 035 $a(PQKBWorkID)10297760 035 $a(PQKB)10536369 035 $a(DE-He213)978-3-540-48161-4 035 $a(MiAaPQ)EBC5577099 035 $a(MiAaPQ)EBC6700787 035 $a(Au-PeEL)EBL5577099 035 $a(OCoLC)1066181133 035 $a(Au-PeEL)EBL6700787 035 $a(PPN)155237993 035 $a(EXLCZ)991000000000437297 100 $a20220429d1999 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic PDE's and Kolmogorov equations in infinite dimensions $electures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, August 24 - September 1, 1998 /$fN. V. Krylov, M. Rockner, J. Zabczyk ; editor, G. Da Prato 205 $a1st ed. 1999. 210 $d©1999. 210 1$aBerlin :$cSpringer,$d[1999] 215 $a1 online resource (XII, 244 p.) 225 1 $aLecture notes in mathematics (Springer-Verlag) ;$v1715 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-66545-5 327 $aN.V. Krylov: On Kolmogorov's equations for finite dimensional diffusions: Solvability of Ito's stochastic equations; Markov property of solution; Conditional version of Kolmogorov's equation; Differentiability of solutions of stochastic equations with respect to initial data; Kolmogorov's equations in the whole space; Some Integral approximations of differential operators; Kolmogorov's equations in domains -- M. Roeckner: LP-analysis of finite and infinite dimensional diffusion operators: Solution of Kolmogorov equations via sectorial forms; Symmetrizing measures; Non-sectorial cases: perturbations by divergence free vector fields; Invariant measures: regularity, existence and uniqueness; Corresponding diffusions and relation to Martingale problems -- J. Zabczyk: Parabolic equations on Hilbert spaces: Heat equation; Transition semigroups; Heat equation with a first order term; General parabolic equations; Regularity and Quiqueness; Parabolic equations in open sets; Applications. 330 $aKolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1715. 606 $aStochastic partial differential equations 615 0$aStochastic partial differential equations. 676 $a519.2 700 $aKrylov$b N. V$g(Nikolai? Vladimirovich),$0441392 702 $aRo?ckner$b Michael$f1956- 702 $aZabczyk$b Jerzy 702 $aDa Prato$b Giuseppe 712 02$aCentro internazionale matematico estivo. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466653603316 996 $aStochastic PDE's and Kolmogorov equations in infinite dimensions$91492041 997 $aUNISA