A Rough Path Perspective on Renormalizatio
Peter Friz (Institut für Mathematik, Technische Universität Berlin)
| Martes, 8 de noviembre, 11:30h. Aula Naranja, ICMAT |
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Abstract
We shall introduce geometric and branched rough paths, following T. Lyons (1998) and M. Gubinelli (2010) respectively. In particular, we revisit / extend the notation of translation operator on these objects. As in Hairer's work (2015) on the renormalization of SDPEs subjected to stationary, if ill-defined noise, we propose a purely algebraic view on the matter. Recent advances in the theory of regularity structures, especially the Hopf algebraic interplay of positive and negative renormalization, are seen to have precise counter-parts in the rough path context. At last, we consider some finite-dimensional stochastic examples which do need renormalization.
