04299nam 22006855 450 991014631180332120250730104900.03-540-48161-310.1007/BFb0092416(CKB)1000000000437297(SSID)ssj0000326949(PQKBManifestationID)12069034(PQKBTitleCode)TC0000326949(PQKBWorkID)10297760(PQKB)10536369(DE-He213)978-3-540-48161-4(MiAaPQ)EBC5577099(MiAaPQ)EBC6700787(Au-PeEL)EBL5577099(OCoLC)1066181133(Au-PeEL)EBL6700787(PPN)155237993(EXLCZ)99100000000043729720121227d1999 u| 0engurnn#008mamaatxtccrStochastic PDE's and Kolmogorov Equations in Infinite Dimensions Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in Cetraro, Italy, August 24 - September 1, 1998 /by N.V. Krylov, M. Röckner, J. Zabczyk ; edited by G. Da Prato1st ed. 1999.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1999.1 online resource (XII, 244 p.)C.I.M.E. Foundation Subseries,2946-1820 ;1715Bibliographic Level Mode of Issuance: Monograph3-540-66545-5 N.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.Kolmogorov 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.C.I.M.E. Foundation Subseries,2946-1820 ;1715ProbabilitiesDifferential equationsProbability TheoryDifferential EquationsProbabilities.Differential equations.Probability Theory.Differential Equations.519.2Krylov N. V(Nikolaĭ Vladimirovich),441392Röckner Michael1956-Zabczyk JerzyDa Prato GiuseppeCentro internazionale matematico estivo.MiAaPQMiAaPQMiAaPQBOOK9910146311803321Stochastic PDE's and Kolmogorov equations in infinite dimensions1492041UNINA