A note on the continuity in the hurst index of the solution of rough differential equations driven by a fractional brownian motion

Abstract

Within the rough path framework, we prove the continuity of the solution to random differential equations driven by a one dimensional fractional Brownian motion with respect to the Hurst parameter H when $H\in (1/3,1/2].$

KEYWORDS:

• Continuity
• hurst parameters
• fractional brownian motion
• rough path

Acknowledgements

The authors would like to thank the anonymous reviewer for the interesting and useful comments, which help to improve the paper.

Additional information

Funding

The first author is funded by the DFG under Germanys Excellence Strategy - GZ 2047/1, project-id 390685813.