Convergence rate in the splitting-up method for rough differential equations

Peter H. C. Pang

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arXiv · 2412.00432

Convergence rate in the splitting-up method for rough differential equations

Peter H. C. Pang

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Abstract

In this note we construct solutions to rough differential equations ${\rm d} Y = f(Y) \,{\rm d} X$ with a driver $X \in C^\alpha([0,T];\mathbb{R}^d)$, $\frac13 < \alpha \le \frac12$, using a splitting-up scheme. We show convergence of our scheme to solutions in the sense of Davie by a new argument and give a rate of convergence.

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BibTeX RIS

Peter H. C. Pang. 2024-11-30. Convergence rate in the splitting-up method for rough differential equations. https://arxiv.org/abs/2412.00432

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