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Multidimensional stochastic processe...

Friz, Peter K., (1974-)

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Multidimensional stochastic processes as rough paths = theory and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Multidimensional stochastic processes as rough paths/ Peter K. Friz, Nicolas B. Victoir.
Reminder of title:	theory and applications /
Author:	Friz, Peter K.,
other author:	Victoir, Nicolas B.
Published:	Cambridge :Cambridge University Press, : 2010.,
Description:	xiv, 656 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	Introduction -- The story in a nutshell -- Continuous paths of bounded variation -- Riemann-Stieltjes integration -- Ordinary differential equations -- ODEs : smoothness -- Variation and Holder spaces -- Young integration -- Free nilpotent groups -- Variation and Holder spaces on free groups -- Geometric rough path spaces -- Rough differential equations -- RDEs : smoothness -- RDEs with drift and other topics -- Brownian motion -- Continuous (semi- )martingales -- Gaussian processes -- Markov processes -- Stochastic differential equations and stochastic flows -- Stochastic Taylor expansions -- Support theorem and large deviations -- Malliavin calculus for RDEs -- Appendix A: Sample paths regularity and related topics -- Appendix B: Banach calculus -- Appendix C: Large deviations -- Appendix D: Gaussian analysis -- Appendix E: Analysis on local Dirichlet spaces.
Subject:	Stochastic difference equations. -
Online resource:	https://doi.org/10.1017/CBO9780511845079
ISBN:	9780511845079

Multidimensional stochastic processes as rough paths = theory and applications /
Friz, Peter K.,1974-

Multidimensional stochastic processes as rough pathstheory and applications /[electronic resource] :Peter K. Friz, Nicolas B. Victoir. - Cambridge :Cambridge University Press,2010. - xiv, 656 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;120. - Cambridge studies in advanced mathematics ;120..

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

Introduction -- The story in a nutshell -- Continuous paths of bounded variation -- Riemann-Stieltjes integration -- Ordinary differential equations -- ODEs : smoothness -- Variation and Holder spaces -- Young integration -- Free nilpotent groups -- Variation and Holder spaces on free groups -- Geometric rough path spaces -- Rough differential equations -- RDEs : smoothness -- RDEs with drift and other topics -- Brownian motion -- Continuous (semi- )martingales -- Gaussian processes -- Markov processes -- Stochastic differential equations and stochastic flows -- Stochastic Taylor expansions -- Support theorem and large deviations -- Malliavin calculus for RDEs -- Appendix A: Sample paths regularity and related topics -- Appendix B: Banach calculus -- Appendix C: Large deviations -- Appendix D: Gaussian analysis -- Appendix E: Analysis on local Dirichlet spaces.

Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.

ISBN: 9780511845079Subjects--Topical Terms:

747375
Stochastic difference equations.

LC Class. No.: QA274.23 / .F746 2010

Dewey Class. No.: 519.2

Multidimensional stochastic processes as rough paths = theory and applications /
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100 1 $a Friz, Peter K., $d 1974- $3 1299059
245 1 0 $a Multidimensional stochastic processes as rough paths $h [electronic resource] : $b theory and applications / $c Peter K. Friz, Nicolas B. Victoir.
260 $a Cambridge : $b Cambridge University Press, $c 2010.
300 $a xiv, 656 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 120
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Introduction -- The story in a nutshell -- Continuous paths of bounded variation -- Riemann-Stieltjes integration -- Ordinary differential equations -- ODEs : smoothness -- Variation and Holder spaces -- Young integration -- Free nilpotent groups -- Variation and Holder spaces on free groups -- Geometric rough path spaces -- Rough differential equations -- RDEs : smoothness -- RDEs with drift and other topics -- Brownian motion -- Continuous (semi- )martingales -- Gaussian processes -- Markov processes -- Stochastic differential equations and stochastic flows -- Stochastic Taylor expansions -- Support theorem and large deviations -- Malliavin calculus for RDEs -- Appendix A: Sample paths regularity and related topics -- Appendix B: Banach calculus -- Appendix C: Large deviations -- Appendix D: Gaussian analysis -- Appendix E: Analysis on local Dirichlet spaces.
520 $a Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.
650 0 $a Stochastic difference equations. $3 747375
650 0 $a Stochastic processes. $3 520663
650 0 $a Random measures. $3 1083919
700 1 $a Victoir, Nicolas B. $3 1299060
830 0 $a Cambridge studies in advanced mathematics ; $v 120. $3 3470404
856 4 0 $u https://doi.org/10.1017/CBO9780511845079