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Multidimensional Stochastic Processes as Rough Paths - Peter K. Friz, Nicolas B. Victoir

Multidimensional Stochastic Processes as Rough Paths

Theory and Applications
Buch | Hardcover
670 Seiten
2010
Cambridge University Press (Verlag)
978-0-521-87607-0 (ISBN)
CHF 155,35 inkl. MwSt
Rough paths may play an important role in the future analysis of stochastic partial differential equations. 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.
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.

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.

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 Hölder spaces; 6. Young integration; Part II. Abstract Theory of Rough Paths: 7. Free nilpotent groups; 8. Variation and Hölder 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.

Reihe/Serie Cambridge Studies in Advanced Mathematics
Zusatzinfo Worked examples or Exercises; 2 Halftones, unspecified; 4 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 160 x 235 mm
Gewicht 1600 g
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 0-521-87607-9 / 0521876079
ISBN-13 978-0-521-87607-0 / 9780521876070
Zustand Neuware
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