Spectral bandwidth under coupling between multiple Ornstein–Uhlenbeck processes

Derive closed-form expressions for the power spectral density and bandwidth of systems composed of multiple coupled two-dimensional Ornstein–Uhlenbeck processes, and characterize how coupling strength modifies the effective width and shape of the frequency spectrum for arbitrary coupling configurations.

Background

The authors extend their model to pairs of weakly coupled Ornstein–Uhlenbeck processes with distinct natural frequencies and provide analytic PSD formulas for certain coupling cases, showing the emergence of multiple spindle types.

They explicitly raise the open question of how coupling generally affects spectral width and shape, and whether closed-form PSD and bandwidth expressions can be derived for arbitrary coupling beyond the specific cases treated.