LEADER 03929nam 22006015 450 001 996466672203316 005 20200706081217.0 010 $a3-540-45147-1 024 7 $a10.1007/b80743 035 $a(CKB)1000000000233202 035 $a(SSID)ssj0000326457 035 $a(PQKBManifestationID)11912759 035 $a(PQKBTitleCode)TC0000326457 035 $a(PQKBWorkID)10267489 035 $a(PQKB)10180918 035 $a(DE-He213)978-3-540-45147-1 035 $a(MiAaPQ)EBC3073202 035 $a(PPN)155213148 035 $a(EXLCZ)991000000000233202 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aSecond Order PDE's in Finite and Infinite Dimension$b[electronic resource] $eA Probabilistic Approach /$fby Sandra Cerrai 205 $a1st ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (XII, 332 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1762 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-42136-X 320 $aIncludes bibliographical references and index. 327 $aKolmogorov equations in Rd with unbounded coefficients -- Asymptotic behaviour of solutions -- Analyticity of the semigroup in a degenerate case -- Smooth dependence on data for the SPDE: the Lipschitz case -- Kolmogorov equations in Hilbert spaces -- Smooth dependence on data for the SPDE: the non-Lipschitz case (I) -- Smooth dependence on data for the SPDE: the non-Lipschitz case (II) -- Ergodicity -- Hamilton- Jacobi-Bellman equations in Hilbert spaces -- Application to stochastic optimal control problems. 330 $aThe main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. We focus our attention on the regularity properties of the solutions and hence on the smoothing effect of the corresponding transition semigroups in the space of bounded and uniformly continuous functions. As an application of these results, we study the associated Kolmogorov equations, the large-time behaviour of the solutions and some stochastic optimal control problems together with the corresponding Hamilton- Jacobi-Bellman equations. In the literature there exists a large number of works (mostly in finite dimen­ sion) dealing with these arguments in the case of bounded Lipschitz-continuous coefficients and some of them concern the case of coefficients having linear growth. Few papers concern the case of non-Lipschitz coefficients, but they are mainly re­ lated to the study of the existence and the uniqueness of solutions for the stochastic system. Actually, the study of any further properties of those systems, such as their regularizing properties or their ergodicity, seems not to be developed widely enough. With these notes we try to cover this gap. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1762 606 $aPartial differential equations 606 $aProbabilities 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aPartial differential equations. 615 0$aProbabilities. 615 14$aPartial Differential Equations. 615 24$aProbability Theory and Stochastic Processes. 676 $a519.2 700 $aCerrai$b Sandra$4aut$4http://id.loc.gov/vocabulary/relators/aut$066299 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466672203316 996 $aSecond order PDE's in finite and infinite dimension$9377806 997 $aUNISA