BibTex format
@unpublished{Cass:2016,
author = {Cass, T and Weidner, MP},
title = {Tree algebras over topological vector spaces in rough path theory},
url = {http://arxiv.org/abs/1604.07352v2},
year = {2016}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - UNPB
AB - We work with non-planar rooted trees which have a label set given by anarbitrary vector space $V$. By equipping $V$ with a complete locally convextopology, we show how a natural topology is induced on the tree algebra over$V$. In this context, we introduce the Grossman-Larson and Connes-Kreimertopological Hopf algebras over $V$, and prove that they form a dual pair in acertain sense. As an application we define the class of branched rough pathsover a general Banach space, and propose a new definition of a solution to arough differential equation (RDE) driven by one of these branched rough paths.We show equivalence of our definition with a Davie-Friz-Victoir-typedefinition, a version of which is widely used for RDEs with geometric drivers,and we comment on applications to RDEs with manifold-valued solutions.
AU - Cass,T
AU - Weidner,MP
PY - 2016///
TI - Tree algebras over topological vector spaces in rough path theory
UR - http://arxiv.org/abs/1604.07352v2
ER -