Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 71, Number 3 (2019), 915-978.
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 semimartingale 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.
The first author was partly supported by the ANR project “Retour Post-doctorant”, no. 11–PDOC-0025. He also thanks the U.B.O. for their hospitality, part of this work was written there. The second author was partly supported by the DFG Research Unit FOR 2402.
J. Math. Soc. Japan, Volume 71, Number 3 (2019), 915-978.
Received: 12 March 2018
First available in Project Euclid: 28 May 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60G44: Martingales with continuous parameter 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]
BAILLEUL, Ismaël; RIEDEL, Sebastian. Rough flows. J. Math. Soc. Japan 71 (2019), no. 3, 915--978. doi:10.2969/jmsj/80108010. https://projecteuclid.org/euclid.jmsj/1559030414