Empirical Transfer Operators and Finite-Sample Change Detection for Noisy Expanding Interval Maps
arXiv:2606.06785v1 Announce Type: cross Abstract: We study finite-sample change detection for one-dimensional noisy dynamical systems using partition-based empirical approximations of stationary behaviour. Given observations from an interval-valued process, we partition the state space, estimate a finite transition matrix from observed transitions between partition elements, and apply a small Doeblin-type regularisation to ensure a unique stationary distribution. From an initial reference segment, we compute a baseline empirical stationary distribution \(\widehat{\pi}_{0,\rho}\). For each late
This is a theoretical paper in the field of dynamical systems and statistical learning, representing incremental academic research rather than a real-world event or breakthrough.
While foundational for future advancements in AI and data analysis, this specific publication does not directly impact strategic readers in the immediate term due to its abstract and theoretical nature.
No immediate real-world changes result from this publication; it contributes to the academic understanding of change detection in noisy systems.
Increased theoretical understanding of change detection in complex systems.
Potential for refined algorithms in anomaly detection or system monitoring in the distant future.
Improved robustness of AI systems dealing with dynamic and uncertain environments, perhaps decades from now.
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