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Rough Paths and Regularity Structures

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  • UserProf P. K. Friz (TU and WIAS, Berlin)
  • ClockThursday 23 April 2015, 14:00-15:00
  • HouseMR14.

If you have a question about this talk, please contact CCA.

Short Course

Rough path analysis has provided new insights in the analysis of stochastic di erential equations and stochastic partial di erential equations. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic di erential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using speci c probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a signi cant extension, Hairer’s theory of regularity structures, and the second half of this course is devoted to a gentle introduction.

Pre-requisite Mathematics

  • Upper undergraduate analysis, interest (and a little maturity) in stochastic analysis.

Literature

1. Terry J. Lyons, Michael Caruana, and Thierry Levy, Di erential equations driven by rough paths, Lecture Notes in Mathematics, vol. 1908, Springer, Berlin, 2007

2. Peter K. Friz, Nicolas Victoir, Multidimensional stochastic processes as rough paths, Cambridge Studies in Advanced Mathematics, vol. 120, Cambridge University Press, Cambridge, 2010

3. Peter K. Friz and Martin Hairer, A course on rough paths: With an introduction to regularity structures, Springer Universitext, 2014.

4. Martin Hairer, A theory of regularity structures, Inventiones mathematicae (2014), 1-236

This talk is part of the Cambridge Centre for Analysis talks series.

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