Open Access
July, 2019 Rough flows
Ismaël BAILLEUL, Sebastian RIEDEL
J. Math. Soc. Japan 71(3): 915-978 (July, 2019). DOI: 10.2969/jmsj/80108010


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.

Funding Statement

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.


Download Citation

Ismaël BAILLEUL. Sebastian RIEDEL. "Rough flows." J. Math. Soc. Japan 71 (3) 915 - 978, July, 2019.


Received: 12 March 2018; Published: July, 2019
First available in Project Euclid: 28 May 2019

zbMATH: 07121559
MathSciNet: MR3984248
Digital Object Identifier: 10.2969/jmsj/80108010

Primary: 34F05 , 60G44 , 60H10

Keywords: rough flows , semimartingale velocity fields , Stochastic flows

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 3 • July, 2019
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