Title: Multidimensional stochastic processes as rough paths : theory and applications /
Authors: Friz, Peter K., 1974-; Victoir, Nicolas B.
Publisher: Cambridge University Press,
Year: 2010
Subjects: Stochastic difference equations.; Stochastic processes.; Random measures.; Stochastic analysis
Abstract: An introduction to rough path theory and its applications to stochastic analysis, written for graduate students and researchers.
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.