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

By: Friz, Peter K, 1974-
Contributor(s): Victoir, Nicolas B
Material type: TextTextSeries: Cambridge studies in advanced mathematics: 120.Publisher: Cambridge, UK ; New York : Cambridge University Press, 2010Description: 1 online resource (xiv, 656 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9780511677540; 0511677545; 9780511682025; 0511682026; 9780511845079; 0511845073; 9780511680045; 051168004XSubject(s): Stochastic difference equations | Stochastic processes | Random measures | MATHEMATICS -- Probability & Statistics -- General | Random measures | Stochastic difference equations | Stochastic processes | Stochastische Differentialgleichung | Stochastischer Prozess | Stochastische Analysis | StochastikGenre/Form: Electronic books. Additional physical formats: Print version:: Multidimensional stochastic processes as rough paths.DDC classification: 519.2 LOC classification: QA274.23 | .F746 2010ebOther classification: SK 820 | MAT 605f Online resources: Click here to access online
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.
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Includes bibliographical references (pages 638-651) and index.

Print version record.

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.

An introduction to rough path theory and its applications to stochastic analysis, written for graduate students and researchers.

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