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001 978-3-540-45147-1
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008 121227s2001 gw | s |||| 0|eng d
020 _a9783540451471
_9978-3-540-45147-1
024 7 _a10.1007/b80743
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.353
_223
245 1 0 _aSecond Order PDE’s in Finite and Infinite Dimension
_h[electronic resource] :
_bA Probabilistic Approach /
_cedited by Sandra Cerrai.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2001.
300 _aXII, 332 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1762
505 0 _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.
520 _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.
650 0 _aDifferential equations, partial.
650 0 _aDistribution (Probability theory.
650 1 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
700 1 _aCerrai, Sandra.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662200377
776 0 8 _iPrinted edition:
_z9783540421368
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1762
856 4 0 _uhttps://doi.org/10.1007/b80743
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10545
_d10545