Conference abstracts

Session A5 - Geometric Integration and Computational Mechanics

July 11, 17:00 ~ 17:30 - Room 111

ROUGH PATHS ON HOMOGENEOUS SPACES

Hans Munthe-Kaas

Bergen, Norway   -   hans.munthe-kaas@uib.no

We consider rough paths in the context of differential equations on homogenous manifolds. Our approach generalises both the Chen-type shuffle algebra of word series underlying Terry Lyons’ theory of rough paths as well as the branched rough paths of Massimiliano Gubinelli, which are based on B-series and the Connes-Kreimer Hopf algebra of rooted trees. The new approach contains these as special cases and extends geometrically to rough paths evolving on homogeneous manifolds.

References:

[1] K. T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. Math. 65 No1, 163–178 (1957).

[2] M. Gubinelli, Ramification of Rough Paths, Journal of Differential Equations 248, no. 4 (2010) 693-721.

[3] T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana 14 No2, 215–310 (1998).

Joint work with Charles Curry (NTNU, Norway), Kurusch Ebrahimi-Fard (NTNU, Norway) and Dominique Manchon (Clermont-Ferrand, France).

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