Conditional independence in stationary distributions of diffusions

Tobias Boege, Mathias Drton, Benjamin Hollering, Sarah Lumpp, Pratik Misra and Daniela Schkoda

Stochastic Processes and their Applications, 2025, vol. 184, issue C

Abstract: Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate diffusion processes with a sparsely structured drift. Our main result gives a characterization of the conditional independence relations that hold in a stationary distribution. The result draws on a graphical representation of the drift structure and pertains to conditional independence relations that hold generally as a consequence of the drift’s sparsity pattern.

Keywords: Conditional independence; Graphical model; Lyapunov equation; Markov process; Ornstein–Uhlenbeck process (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104604

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