Extension of the OU spindle framework to non-Gaussian perturbations

Extend the two-dimensional Ornstein–Uhlenbeck spindle-generating framework to incorporate non-Gaussian perturbations, including Lévy noise and state-dependent diffusion, and characterize resulting heavy-tailed statistics in spindle features and their dependence on model parameters.

Background

The current modeling relies on Gaussian white noise driving the Ornstein–Uhlenbeck dynamics to produce transient spindles whose features are statistically tractable.

The authors explicitly raise the open problem of generalizing the framework to non-Gaussian or state-dependent noise to account for heavy tails observed in some neural systems, which would require new analytic tools and may alter spindle statistics.

References

Despite the progress offered by our model, several computational and segmentation questions remain open: Extension to non-Gaussian noise: Can this framework be generalized to include non-Gaussian perturbations (e.g., Lévy noise or state-dependent diffusion) to model heavy-tailed statistics observed in certain neural systems?

— Modeling, Segmenting and Statistics of Transient Spindles via Two-Dimensional Ornstein-Uhlenbeck Dynamics (2512.10844 - Sun et al., 11 Dec 2025) in Section 7, Discussion and Open Problems