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arXiv · 2603.07675

Rough differential equations driven by TFBM with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$

Lijuan Zhang·Jianhua Huang
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Abstract

We consider the rough differential equations driven by tempered fractional Brownian motion with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$ and tempered parameter $\lambda>0$. First, by means of piecewise linear approximation, we canonically lift the tempered fractional Brownian motion to a three-step geometric rough path in an almost sure sense. Subsequently, employing the Doss-Sussmann technique in conjunction with a greedy sequence of stopping times, we construct a suitable transformation that establishes a bijection between the solution of the rough differential equation and that of an associated ordinary differential equation. This yields the existence and uniqueness of a solution to the original equation. Based on this result and appealing to Gronwall's lemma, we further derive an upper bound for the solution norm, thereby providing a quantitative control on its growth.

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Lijuan Zhang, Jianhua Huang. 2026-03-08. Rough differential equations driven by TFBM with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$. https://arxiv.org/abs/2603.07675

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