Flow techniques for non-geometric RDEs on manifolds
Probability
2023-12-19 v3 Classical Analysis and ODEs
Abstract
In 2015, Bailleul presented a mechanism to solve rough differential equations by constructing flows, using the log-ODE method. We extend this notion in two ways: On the one hand, we localize Bailleul's notion of an almost-flow to solve RDEs on manifolds. On the other hand, we extend his results to non-geometric rough paths, living in any connected, cocommutative, graded Hopf algebra. This requires a new concept, which we call a pseudo bialgebra map. We further connect our results to Curry et al (2020), who solved planarly branched RDEs on homogeneous spaces.
Cite
@article{arxiv.2310.13556,
title = {Flow techniques for non-geometric RDEs on manifolds},
author = {Hannes Kern and Terry Lyons},
journal= {arXiv preprint arXiv:2310.13556},
year = {2023}
}