000 | 03592nam a22004815i 4500 | ||
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001 | 978-3-540-45147-1 | ||
003 | DE-He213 | ||
005 | 20190213151411.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s2001 gw | s |||| 0|eng d | ||
020 |
_a9783540451471 _9978-3-540-45147-1 |
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024 | 7 |
_a10.1007/b80743 _2doi |
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050 | 4 | _aQA370-380 | |
072 | 7 |
_aPBKJ _2bicssc |
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072 | 7 |
_aMAT007000 _2bisacsh |
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072 | 7 |
_aPBKJ _2thema |
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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. |
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300 |
_aXII, 332 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1762 |
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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 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/b80743 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
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_c10545 _d10545 |