Rough differential equations driven by TFBM with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914378720215040 |
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| author | Zhang, Lijuan Huang, Jianhua |
| author_facet | Zhang, Lijuan Huang, Jianhua |
| contents | 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 $λ>0$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07675 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rough differential equations driven by TFBM with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$ Zhang, Lijuan Huang, Jianhua Dynamical Systems Probability 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 $λ>0$. 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. |
| title | Rough differential equations driven by TFBM with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$ |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2603.07675 |