000			04680nam a22005535i 4500
001			978-0-387-89488-1
003			DE-He213
005			20140220084456.0
007			cr nn 008mamaa
008			100301s2010 xxu| s |||| 0|eng d
020			_a9780387894881 _9978-0-387-89488-1
024	7		_a10.1007/978-0-387-89488-1 _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		_aHolden, Helge. _eauthor.
245	1	0	_aStochastic Partial Differential Equations _h[electronic resource] : _bA Modeling, White Noise Functional Approach / _cby Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang.
264		1	_aNew York, NY : _bSpringer New York, _c2010.
300			_bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_aPreface to the Second Edition -- Preface to the First Edition -- Introduction -- Framework -- Applications to stochastic ordinary differential equations -- Stochastic partial differential equations driven by Brownian white noise -- Stochastic partial differential equations driven by Lévy white noise -- Appendix A. The Bochner-Minlos theorem -- Appendix B. Stochastic calculus based on Brownian motion -- Appendix C. Properties of Hermite polynomials -- Appendix D. Independence of bases in Wick products -- Appendix E. Stochastic calculus based on Lévy processes- References -- List of frequently used notation and symbols -- Index.
520			_aThe first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by space-time Brownian motion noise. In this, the second edition, the authors extend the theory to include SPDEs driven by space-time Lévy process noise, and introduce new applications of the field. Because the authors allow the noise to be in both space and time, the solutions to SPDEs are usually of the distribution type, rather than a classical random field. To make this study rigorous and as general as possible, the discussion of SPDEs is therefore placed in the context of Hida white noise theory. The key connection between white noise theory and SPDEs is that integration with respect to Brownian random fields can be expressed as integration with respect to the Lebesgue measure of the Wick product of the integrand with Brownian white noise, and similarly with Lévy processes. The first part of the book deals with the classical Brownian motion case. The second extends it to the Lévy white noise case. For SPDEs of the Wick type, a general solution method is given by means of the Hermite transform, which turns a given SPDE into a parameterized family of deterministic PDEs. Applications of this theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter. From the reviews of the first edition: "The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully written and the details of the proofs are basically spelled out... This is a rich and demanding book… It will be of great value for students of probability theory or SPDEs with an interest in the subject, and also for professional probabilists." —Mathematical Reviews "...a comprehensive introduction to stochastic partial differential equations." —Zentralblatt MATH
650		0	_aMathematics.
650		0	_aDifferential Equations.
650		0	_aDifferential equations, partial.
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	_aOrdinary Differential Equations.
650	2	4	_aMathematical Modeling and Industrial Mathematics.
700	1		_aØksendal, Bernt. _eauthor.
700	1		_aUbøe, Jan. _eauthor.
700	1		_aZhang, Tusheng. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387894874
830		0	_aUniversitext
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-89488-1
912			_aZDB-2-SMA
999			_c109855 _d109855