Rough flows
Abstract
We introduce in this work a concept of rough driver that somehow provides a rough path-like analogue of an enriched object associated with time-dependent vector fields. We use the machinery of approximate flows to build the integration theory of rough drivers and prove well-posedness results for rough differential equations on flows and continuity of the solution flow as a function of the generating rough driver. We show that the theory of semi-martingale stochastic flows developed in the 80's and early 90's fits nicely in this framework, and obtain as a consequence some strong approximation results for general semimartingale flows and provide a fresh look at large deviation theorems for 'Gaussian' stochastic flows.
Keywords
Cite
@article{arxiv.1505.01692,
title = {Rough flows},
author = {I. Bailleul and S. Riedel},
journal= {arXiv preprint arXiv:1505.01692},
year = {2018}
}
Comments
v4, 55 pages; final version. The exposition has been polished to make the work easier to read