Based on two isomorphisms of Hopf algebras, we provide a bound in the optimal order on the remainder of the truncated Taylor expansion for controlled differential equations driven by branched rough paths.
The author gratefully acknowledge the support of the National Natural Science Foundation of China (Young Scholar Grant 12201081), Chongqing University (Starting Grant 02080011044104) and EPSRC (Programme Grant EP/S026347/1).
"A remainder estimate for branched rough differential equations." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/22-ECP473