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SUMMARY:Rough Paths and Regularity Structures - Prof P. K. Friz (TU and WI
 AS\, Berlin)
DTSTART:20150506T150000Z
DTEND:20150506T170000Z
UID:TALK54733@talks.cam.ac.uk
CONTACT:CCA
DESCRIPTION:Rough path analysis has provided new insights in the analysis 
 of stochastic dierential equations and stochastic partial dierential equ
 ations. 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 dierential equations and p
 rovides a clean break between analytical and probabilistic arguments. It p
 rovides 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 e
 xtension\, Hairer’s theory of regularity structures\, and the second hal
 f of this course is devoted to a gentle introduction.\n\nPre-requisite Mat
 hematics\n\n* Upper undergraduate analysis\, interest (and a little maturi
 ty) in stochastic analysis.\n\nLiterature\n\n1. Terry J. Lyons\, Michael C
 aruana\, and Thierry Levy\, Dierential equations driven by rough paths\, 
 Lecture Notes in Mathematics\, vol. 1908\, Springer\, Berlin\, 2007\n\n2. 
 Peter K. Friz\, Nicolas Victoir\, Multidimensional stochastic processes as
  rough paths\, Cambridge Studies in Advanced Mathematics\, vol. 120\, Camb
 ridge University Press\, Cambridge\, 2010\n\n3. Peter K. Friz and Martin H
 airer\, A course on rough paths: With an introduction to regularity struct
 ures\, Springer Universitext\, 2014.\n\n4. Martin Hairer\, A theory of reg
 ularity structures\, Inventiones mathematicae (2014)\, 1-236
LOCATION:MR14
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