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SUMMARY:Rough Paths and Regularity Structures - Prof P. K. Friz (TU and WI
 AS\, Berlin)
DTSTART:20150422T150000Z
DTEND:20150422T170000Z
UID:TALK54731@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\nmartingal
 e 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.\n\nPre-requisite Math
 ematics\n* Upper undergraduate analysis\, interest (and a little maturity)
  in stochastic analysis. \n\nLiterature\n\n1. Terry J. Lyons\, Michael Car
 uana\, and Thierry Levy\, Dierential equations driven by rough paths\, Le
 cture Notes in Mathematics\, vol. 1908\, Springer\, Berlin\, 2007\n\n2. Pe
 ter K. Friz\, Nicolas Victoir\, Multidimensional stochastic processes as r
 ough paths\, Cambridge Studies in Advanced Mathematics\, vol. 120\, Cambri
 dge University Press\, Cambridge\, 2010\n\n3. Peter K. Friz and Martin Hai
 rer\, A course on rough paths: With an introduction to regularity structur
 es\, Springer Universitext\, 2014.\n\n4. Martin Hairer\, A theory of regul
 arity structures\, Inventiones mathematicae (2014)\, 1-236 
LOCATION:MR14
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