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001			978-3-540-70781-3
003			DE-He213
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008			100301s2007 gw | s |||| 0|eng d
020			_a9783540707813 _9978-3-540-70781-3
024	7		_a10.1007/978-3-540-70781-3 _2doi
050		4	_aQA299.6-433
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
072		7	_aPBK _2thema
082	0	4	_a515 _223
100	1		_aPrévôt, Claudia. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	2	_aA Concise Course on Stochastic Partial Differential Equations _h[electronic resource] / _cby Claudia Prévôt, Michael Röckner.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2007.
300			_aVI, 148 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 ; _v1905
505	0		_aMotivation, Aims and Examples -- Stochastic Integral in Hilbert spaces -- Stochastic Differential Equations in Finite Dimensions -- A Class of Stochastic Differential Equations in Banach Spaces -- Appendices: The Bochner Integral -- Nuclear and Hilbert-Schmidt Operators -- Pseudo Invers of Linear Operators -- Some Tools from Real Martingale Theory -- Weak and Strong Solutions: the Yamada-Watanabe Theorem -- Strong, Mild and Weak Solutions.
520			_aThese lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.
650		0	_aGlobal analysis (Mathematics).
650		0	_aDifferential equations, partial.
650		0	_aDistribution (Probability theory.
650	1	4	_aAnalysis. _0http://scigraph.springernature.com/things/product-market-codes/M12007
650	2	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		_aRöckner, Michael. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540835288
776	0	8	_iPrinted edition: _z9783540707806
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v1905
856	4	0	_uhttps://doi.org/10.1007/978-3-540-70781-3
912			_aZDB-2-SMA
912			_aZDB-2-LNM
999			_c10676 _d10676