Multidimensional Stochastic Processes as Rough Paths
Theory and Applications
Published on 4. February 2010
Book
Hardback
670 pages
978-0-521-87607-0 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises; 2 Halftones, unspecified; 4 Line drawings, unspecified
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 40 mm
Weight
1108 gr
ISBN-13
978-0-521-87607-0 (9780521876070)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Peter K. Friz | Nicolas B. Victoir
Multidimensional Stochastic Processes as Rough Paths
Theory and Applications
E-Book
04/2010
1st Edition
Cambridge University Press
€94.99
Available for download
Persons
Peter K. Friz is a Reader in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He is also a Research Group Leader at the Johann Radon Institute at the Austrian Academy of Sciences, Linz. Nicolas B. Victoir works in quantitative research at JPMorgan in Hong Kong.
Content
Preface; Introduction; The story in a nutshell; Part I. Basics: 1. Continuous paths of bounded variation; 2. Riemann-Stieltjes integration; 3. Ordinary differential equations (ODEs); 4. ODEs: smoothness; 5. Variation and Hoelder spaces; 6. Young integration; Part II. Abstract Theory of Rough Paths: 7. Free nilpotent groups; 8. Variation and Hoelder spaces on free groups; 9. Geometric rough path spaces; 10. Rough differential equations (RDEs); 11. RDEs: smoothness; 12. RDEs with drift and other topics; Part III. Stochastic Processes Lifted to Rough Paths: 13. Brownian motion; 14. Continuous (semi)martingales; 15. Gaussian processes; 16. Markov processes; Part IV. Applications to Stochastic Analysis: 17. Stochastic differential equations and stochastic flows; 18. Stochastic Taylor expansions; 19. Support theorem and large deviations; 20. Malliavin calculus for RDEs; Part V. Appendix: A. Sample path regularity and related topics; B. Banach calculus; C. Large deviations; D. Gaussian analysis; E. Analysis on local Dirichlet spaces; Frequently used notation; References; Index.