# Multidimensional Stochastic Processes as Rough Paths: Theory and Applications

@inproceedings{Friz2010MultidimensionalSP, title={Multidimensional Stochastic Processes as Rough Paths: Theory and Applications}, author={Peter K. Friz and Nicolas Victoir}, year={2010} }

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 Holder 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…

## 404 Citations

Topics in Stochastic Analysis and Riemannian Foliations

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This work proves the existence and regularity of local center manifolds for RDEs by means of a suitably discretized Lyapunov-Perron-type method and connects the rough path / regularity structures, ODE and random dynamical systems approaches.

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- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
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. Given a solution Y to a rough differential equation (RDE), a recent result ( Ann. Probab. 47 (2019) 1–60) extends the classical Itô-Stratonovich formula and provides a closed-form expression for…

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