MA694 Rough paths theory

During the Spring 2013 semester I will teach a class on rough paths theory and post the lectures on this blog.

The rough paths theory was discovered by Terry Lyons in the 1990’s. The theory allows to solve differential equations driven by rough signals. The theory is deterministic but perfectly applies to the study of differential equations driven by rough random signals as the Brownian motion or even potentially rougher signals such as the fractional Brownian motion. The main reference for the course will be the book:

P. Friz, N. Victoir: Multidimensional stochastic processes as rough paths. Theory and Applications. Cambridge Studies in Advanced Mathematics (CUP, 2009)

A rough table of contents is as follows:

  • Ordinary differential equations
  • Young’s integration theory
  • Estimating iterated integrals
  • p-rough paths
  • Rough linear differential equations
  • Carnot groups
  • Geometric rough paths
  • Rough differential equations
  • Stochastic processes as rough paths
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2 Responses to MA694 Rough paths theory

  1. alabair says:

    A warm thaks for your replay. I think it would be appropriate to give us more details concerning the above noted subject. And write a new blogs for each theme montined.

  2. Tar says:

    I am reading ath the moment Fritz&Victoir and find some proofs or explanations to be to complicated. Hope your blog will help me to clarify some places in this book. Best wishes

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