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The Resource Multidimensional stochastic processes as rough paths : theory and applications, Peter K. Friz, Nicolas B. Victoir

Multidimensional stochastic processes as rough paths : theory and applications, Peter K. Friz, Nicolas B. Victoir

Label
Multidimensional stochastic processes as rough paths : theory and applications
Title
Multidimensional stochastic processes as rough paths
Title remainder
theory and applications
Statement of responsibility
Peter K. Friz, Nicolas B. Victoir
Creator
Contributor
Author
Subject
Language
eng
Summary
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
Member of
Cataloging source
UkCbUP
http://library.link/vocab/creatorDate
1974-
http://library.link/vocab/creatorName
Friz, Peter K.
Dewey number
519.2
Index
index present
LC call number
QA274.23
LC item number
.F746 2010
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Victoir, Nicolas B.
Series statement
Cambridge studies in advanced mathematics
Series volume
120
http://library.link/vocab/subjectName
  • Stochastic difference equations
  • Stochastic processes
  • Random measures
Label
Multidimensional stochastic processes as rough paths : theory and applications, Peter K. Friz, Nicolas B. Victoir
Instantiates
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- The story in a nutshell -- Continuous paths of bounded variation -- Riemann-Stieltjes integration -- Ordinary differential equations -- ODEs : smoothness -- Variation and Hölder spaces -- Young integration -- Free nilpotent groups -- Variation and Hölder 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
Control code
CR9780511845079
Extent
1 online resource (xiv, 656 pages)
Form of item
online
Isbn
9780511845079
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote
Label
Multidimensional stochastic processes as rough paths : theory and applications, Peter K. Friz, Nicolas B. Victoir
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- The story in a nutshell -- Continuous paths of bounded variation -- Riemann-Stieltjes integration -- Ordinary differential equations -- ODEs : smoothness -- Variation and Hölder spaces -- Young integration -- Free nilpotent groups -- Variation and Hölder 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
Control code
CR9780511845079
Extent
1 online resource (xiv, 656 pages)
Form of item
online
Isbn
9780511845079
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote

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