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

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 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.

Citation

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Ismaël BAILLEUL. Sebastian RIEDEL. "Rough flows." J. Math. Soc. Japan 71 (3) 915 - 978, July, 2019. https://doi.org/10.2969/jmsj/80108010

Information

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

Subjects:
Primary: 34F05, 60G44, 60H10

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 3 • July, 2019
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