000			03645nam a22003858i 4500
001			CR9781139060110
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			110406s2012||||enk o ||1 0|eng|d
020			_a9781139060110 (ebook)
020			_z9781107016149 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA274 _b.O87 2012
082	0	0	_a519.2/3 _223
100	1		_aOsswald, Horst, _eauthor.
245	1	0	_aMalliavin calculus for Lévy processes and infinite-dimensional Brownian motion : _ban introduction / _cHorst Osswald.
246	3		_aMalliavin Calculus for Lévy Processes & Infinite-Dimensional Brownian Motion
264		1	_aCambridge : _bCambridge University Press, _c2012.
300			_a1 online resource (xix, 407 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v191
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aMartingales -- Fourier and Laplace transformations -- Abstract Wiener-Fréchet spaces -- Two concepts of no-anticipation in time -- Malliavin calculus on the space of real sequences -- Introduction to poly-saturated models of mathematics -- Extension of the real numbers -- Topology -- Measure and integration on Loeb spaces -- From finite- to infinite-dimensional Brownian motion -- The Itô integral for infinite-dimensional Brownian motion -- Multiple integrals -- Infinite-dimensional Ornstein-Uhlenbeck processes -- Lindstrøm's construction of standard Lévy processes from discrete ones -- Stochastic integration for Lévy processes -- Chaos decomposition (for infinite-dimensional Brownian motion) -- The Malliavin derivative -- The Skorohod integral -- The interplay between derivative and integral -- Skorohod integral processes -- Girsanov transformations -- Malliavin calculus for Lévy processes (Chaos, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes, Smooth representations, a communication rule for derivative and limit, product-, chainrule, Girsanov transformations) -- Poly-saturated models -- The existence of poly-saturated models.
520			_aAssuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein-Uhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques.
650		0	_aMalliavin calculus.
650		0	_aLévy processes.
650		0	_aBrownian motion processes.
776	0	8	_iPrint version: _z9781107016149
830		0	_aCambridge tracts in mathematics ; _v191.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139060110
999			_c517847 _d517845