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Conditional independence in stationary distributions of diffusions

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

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.

Suggested Citation

  • Boege, Tobias & Drton, Mathias & Hollering, Benjamin & Lumpp, Sarah & Misra, Pratik & Schkoda, Daniela, 2025. "Conditional independence in stationary distributions of diffusions," Stochastic Processes and their Applications, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:spapps:v:184:y:2025:i:c:s0304414925000456
    DOI: 10.1016/j.spa.2025.104604
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    References listed on IDEAS

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    1. Mathias Drton & Thomas S. Richardson, 2008. "Binary models for marginal independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 287-309, April.
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