000 03609nam a22005295i 4500
001 978-3-642-16194-0
003 DE-He213
005 20140220083748.0
007 cr nn 008mamaa
008 101127s2011 gw | s |||| 0|eng d
020 _a9783642161940
_9978-3-642-16194-0
024 7 _a10.1007/978-3-642-16194-0
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aGawarecki, Leszek.
_eauthor.
245 1 0 _aStochastic Differential Equations in Infinite Dimensions
_h[electronic resource] :
_bwith Applications to Stochastic Partial Differential Equations /
_cby Leszek Gawarecki, Vidyadhar Mandrekar.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aXVI, 292 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProbability and Its Applications,
_x1431-7028
505 0 _aPreface -- Part I: Stochastic Differential Equations in Infinite Dimensions -- 1.Partial Differential Equations as Equations in Infinite -- 2.Stochastic Calculus -- 3.Stochastic Differential Equations -- 4.Solutions by Variational Method -- 5.Stochastic Differential Equations with Discontinuous Drift -- Part II: Stability, Boundedness, and Invariant Measures -- 6.Stability Theory for Strong and Mild Solutions -- 7.Ultimate Boundedness and Invariant Measure -- References -- Index.
520 _aThe systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aFinance.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aPartial Differential Equations.
650 2 4 _aQuantitative Finance.
650 2 4 _aApplications of Mathematics.
700 1 _aMandrekar, Vidyadhar.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642161933
830 0 _aProbability and Its Applications,
_x1431-7028
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-16194-0
912 _aZDB-2-SMA
999 _c107126
_d107126