Euler scheme for stochastic functional differential equations driven by fractional Brownian motion
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917378602827776 |
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| author | Garzón, Johanna León, Jorge A. Lozada, Jorge Torres, Soledad |
| author_facet | Garzón, Johanna León, Jorge A. Lozada, Jorge Torres, Soledad |
| contents | In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic integral is the Young one and the coefficient is evaluated in the set of $λ$-Hölder continuous functions on $[-τ,0]$, for some suitable $τ>0$ and $λ\in(1/2,H)$. The rate of convergence of our scheme is $1/n^γ$, for any $γ<2λ-1$. Also, numerical simulations are provided to illustrate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01336 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Euler scheme for stochastic functional differential equations driven by fractional Brownian motion Garzón, Johanna León, Jorge A. Lozada, Jorge Torres, Soledad Probability 34K07, 65C30 In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic integral is the Young one and the coefficient is evaluated in the set of $λ$-Hölder continuous functions on $[-τ,0]$, for some suitable $τ>0$ and $λ\in(1/2,H)$. The rate of convergence of our scheme is $1/n^γ$, for any $γ<2λ-1$. Also, numerical simulations are provided to illustrate our theoretical results. |
| title | Euler scheme for stochastic functional differential equations driven by fractional Brownian motion |
| topic | Probability 34K07, 65C30 |
| url | https://arxiv.org/abs/2604.01336 |