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.
Inhaltsangabe
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.
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.
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