Work

A time-fractional Kalman filter

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.25164

Authors: Draouil, Olfa, Hachemi, Rahma Yasmina Moulay, Øksendal, Bernt, Aliane, Abderrahmen

Institutions: Tunis El Manar University, University of Oslo

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204491186

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