One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady State

We study the problem of recovering the parameters of a multivariate Ornstein-Uhlenbeck (OU) process from steady-state observational and interventional data. In many applications, such as large-scale gene perturbation experiments, only stationary "snapshot" measurements are available, making standard stochastic differential equation estimation methods that rely on time-series trajectories inapplicable. We first establish an identifiability result: one intervention per strongly connected component (SCC) of the drift graph suffices to recover all OU process parameters generically up to a global scaling factor. This holds provided that the SCC condensation graph is connected with a single roo...

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