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
Resource Information
The item Multidimensional stochastic processes as rough paths : theory and applications, Peter K. Friz, Nicolas B. Victoir represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Multidimensional stochastic processes as rough paths : theory and applications, Peter K. Friz, Nicolas B. Victoir represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (xiv, 656 pages)
- Note
- Title from publisher's bibliographic system (viewed on 05 Oct 2015)
- 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
- Isbn
- 9780511845079
- 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
- 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
- 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
- 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
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Multidimensional-stochastic-processes-as-rough/xtSOwuTAXN8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Multidimensional-stochastic-processes-as-rough/xtSOwuTAXN8/">Multidimensional stochastic processes as rough paths : theory and applications, Peter K. Friz, Nicolas B. Victoir</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
