000			02825nam a22004575i 4500
001			978-3-540-29021-6
003			DE-He213
005			20161121231031.0
007			cr nn 008mamaa
008			100301s2006 gw | s |||| 0|eng d
020			_a9783540290216 _9978-3-540-29021-6
024	7		_a10.1007/3-540-29021-4 _2doi
050		4	_aQA319-329.9
072		7	_aPBKF _2bicssc
072		7	_aMAT037000 _2bisacsh
082	0	4	_a515.7 _223
100	1		_aPrato, Giuseppe Da. _eauthor.
245	1	3	_aAn Introduction to Infinite-Dimensional Analysis _h[electronic resource] / _cby Giuseppe Da Prato.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2006.
300			_aX, 208 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aGaussian measures in Hilbert spaces -- The Cameron–Martin formula -- Brownian motion -- Stochastic perturbations of a dynamical system -- Invariant measures for Markov semigroups -- Weak convergence of measures -- Existence and uniqueness of invariant measures -- Examples of Markov semigroups -- L2 spaces with respect to a Gaussian measure -- Sobolev spaces for a Gaussian measure -- Gradient systems.
520			_aIn this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension. Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.
650		0	_aMathematics.
650		0	_aFunctional analysis.
650		0	_aPartial differential equations.
650		0	_aProbabilities.
650	1	4	_aMathematics.
650	2	4	_aFunctional Analysis.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aPartial Differential Equations.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540290209
856	4	0	_uhttp://dx.doi.org/10.1007/3-540-29021-4
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c507578 _d507578