Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 35 min ago
PreprintCC BY 4.0HAL

Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion via Fractional Calculus Techniques

  • Alexander Abreu
  • Héctor Araya
  • Lisandro Fermin
  • Johanna Garzón
  • Soledad Torres
Open at sourcePDFDOICite

Abstract

We study a stochastic functional differential equation (SFDE) with memory driven by a fractional Brownian motion (fBm) with Hurst parameter H > 1/2. An Euler-type numerical scheme is proposed and analyzed under suitable regularity conditions on the drift and diffusion coefficients using tools from fractional calculus. We prove the convergence of the scheme and derive the corresponding rate in terms of the discretization step. Numerical simulations illustrate the theoretical results and confirm the accuracy of the proposed method.

Related

  1. Consistency and Convergence of the Backward-Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion
    Alexander Abreu, Lisandro Fermin, Ernesto Mordecki +1
    HALPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingProbabilityHALarXiv
  2. High-order fractional linear differential equations do not describe stochastic processes with finite state space
    P. Van Mieghem
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsDynamical systemsarXiv
  3. Strong uniqueness for fractional stochastic differential equations with sign drift
    Ercan Sönmez, Yuliya Mishura
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Stationary solution for a fractional stochastic delay differential equations with multiple delays
    Álvaro Guinea Juliá, Alet Roux
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  5. Inference for stochastic differential equations driven by weighted sub-fractional Brownian motion using neural networks and the Euler approximation
    J. H. Ramirez-Gonzalez
    arXivPreprintCC0Full textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{abreu2026euler,
  title = {{Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion via Fractional Calculus Techniques}},
  author = {Alexander Abreu and Héctor Araya and Lisandro Fermin and Johanna Garzón and Soledad Torres},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.05195},
  eprint = {2606.05195},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05578304v3},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion via Fractional Calculus Techniques
AU  - Alexander Abreu
AU  - Héctor Araya
AU  - Lisandro Fermin
AU  - Johanna Garzón
AU  - Soledad Torres
PY  - 2026
DA  - 2026/09/21
PB  - HAL
DO  - 10.48550/arxiv.2606.05195
UR  - https://hal.science/hal-05578304v3
AB  - We study a stochastic functional differential equation (SFDE) with memory driven by a fractional Brownian motion (fBm) with Hurst parameter H > 1/2. An Euler-type numerical scheme is proposed and analyzed under suitable regularity conditions on the drift and diffusion coefficients using tools from fractional calculus. We prove the convergence of the scheme and derive the corresponding rate in terms of the discretization step. Numerical simulations illustrate the theoretical results and confirm the accuracy of the proposed method.
ER  -