A time-fractional Kalman filter

Olfa Draouil; Rahma Yasmina Moulay Hachemi; Bernt Øksendal; Abderrahmen Aliane

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arXiv · 2608.25164

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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Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt Øksendal, Abderrahmen Aliane. 2026-08-25. A time-fractional Kalman filter. https://arxiv.org/abs/2608.25164

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