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PreprintarXiv licencearXiv

A time-fractional Kalman filter

  • Olfa Draouil
  • Rahma Yasmina Moulay Hachemi
  • Bernt Øksendal
  • Abderrahmen Aliane
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Abstract

We study a linear filtering problem in which the signal process is described by a time-fractional linear stochastic differential equation driven by Brownian motion. We derive a stochastic integral equation for the conditional mean alongside a Riccati--Volterra type integral equation for the mean-square error function. As a core application, we introduce a time-fractional state-estimation framework for modelling learning trajectories in children with developmental dyscalculia.

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Cite

BibTeXRIS
BibTeX
@misc{draouil2026timefractional,
  title = {{A time-fractional Kalman filter}},
  author = {Olfa Draouil and Rahma Yasmina Moulay Hachemi and Bernt Øksendal and Abderrahmen Aliane},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.25164},
  eprint = {2608.25164},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.25164},
}
RIS
TY  - UNPB
TI  - A time-fractional Kalman filter
AU  - Olfa Draouil
AU  - Rahma Yasmina Moulay Hachemi
AU  - Bernt Øksendal
AU  - Abderrahmen Aliane
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.25164
UR  - https://arxiv.org/abs/2608.25164
AB  - We study a linear filtering problem in which the signal process is described by a time-fractional linear stochastic differential equation driven by Brownian motion. We derive a stochastic integral equation for the conditional mean alongside a Riccati--Volterra type integral equation for the mean-square error function. As a core application, we introduce a time-fractional state-estimation framework for modelling learning trajectories in children with developmental dyscalculia.
ER  -