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Malliavin calculus for Levy processe...

Osswald, Horst.

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Malliavin calculus for Levy processes and infinite-dimensional Brownian motion = an introduction /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Malliavin calculus for Levy processes and infinite-dimensional Brownian motion/ Horst Osswald.
其他題名:	an introduction /
其他題名:	Malliavin Calculus for Levy Processes & Infinite-Dimensional Brownian Motion
作者:	Osswald, Horst.
出版者:	Cambridge :Cambridge University Press, : 2012.,
面頁冊數:	xix, 407 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	Martingales -- Fourier and Laplace transformations -- Abstract Wiener-Frechet 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 Ito integral for infinite-dimensional Brownian motion -- Multiple integrals -- Infinite-dimensional Ornstein-Uhlenbeck processes -- Lindstrom's construction of standard Levy processes from discrete ones -- Stochastic integration for Levy 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 Levy 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.
標題:	Malliavin calculus. -
電子資源:	https://doi.org/10.1017/CBO9781139060110
ISBN:	9781139060110

Malliavin calculus for Levy processes and infinite-dimensional Brownian motion = an introduction /
Osswald, Horst.

Malliavin calculus for Levy processes and infinite-dimensional Brownian motionan introduction /[electronic resource] :Malliavin Calculus for Levy Processes & Infinite-Dimensional Brownian MotionHorst Osswald. - Cambridge :Cambridge University Press,2012. - xix, 407 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;191. - Cambridge tracts in mathematics ;191..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Martingales -- Fourier and Laplace transformations -- Abstract Wiener-Frechet 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 Ito integral for infinite-dimensional Brownian motion -- Multiple integrals -- Infinite-dimensional Ornstein-Uhlenbeck processes -- Lindstrom's construction of standard Levy processes from discrete ones -- Stochastic integration for Levy 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 Levy 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.

Assuming 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, Levy 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.

ISBN: 9781139060110Subjects--Topical Terms:

648160
Malliavin calculus.

LC Class. No.: QA274 / .O87 2012

Dewey Class. No.: 519.23

Malliavin calculus for Levy processes and infinite-dimensional Brownian motion = an introduction /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Martingales -- Fourier and Laplace transformations -- Abstract Wiener-Frechet 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 Ito integral for infinite-dimensional Brownian motion -- Multiple integrals -- Infinite-dimensional Ornstein-Uhlenbeck processes -- Lindstrom's construction of standard Levy processes from discrete ones -- Stochastic integration for Levy 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 Levy 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 $a Assuming 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, Levy 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 $a Malliavin calculus. $3 648160
650 0 $a Levy processes. $3 747418
650 0 $a Brownian motion processes. $3 646794
830 0 $a Cambridge tracts in mathematics ; $v 191. $3 3470482
856 4 0 $u https://doi.org/10.1017/CBO9781139060110