内容

目次

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 andHolder spaces; 6. Young integration; Part II. Abstract Theory of Rough Paths:7. Free nilpotent groups; 8. Variation and Holder 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. StochasticProcesses 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 equationsand stochastic flows; 18. Stochastic Taylor expansions; 19. Support theoremand large deviations; 20. Malliavin calculus for RDEs; Part V. Appendix: A.Sample path regularity and related topics; B. Banach calculus; C. Largedeviations; D. Gaussian analysis; E. Analysis on local Dirichlet spaces;Frequently used notation; References; Index.