Title Multidimensional stochastic processes as rough paths : theory and applications / Peter K. Friz, Nicolas B. Victoir

Published Cambridge, UK ; New York : Cambridge University Press, 2010

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Description 1 online resource (xiv, 656 pages) : illustrations Series Cambridge studies in advanced mathematics ; 120 Cambridge studies in advanced mathematics ; 120. 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 Summary An introduction to rough path theory and its applications to stochastic analysis, written for graduate students and researchers Bibliography Includes bibliographical references (pages 638-651) and index Notes Print version record Subject Stochastic difference equations. Stochastic processes. Random measures. MATHEMATICS -- Probability & Statistics -- General. Random measures Stochastic difference equations Stochastic processes Stochastische Differentialgleichung Stochastischer Prozess Stochastische Analysis Stochastik Form Electronic book Author Victoir, Nicolas B. ISBN 9780511677540 0511677545 9780511682025 0511682026 9780511845079 0511845073 9780511680045 051168004X

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