Causal interpretation of stochastic differential equations

Abstract

We give a causal interpretation of stochastic differential equations (SDEs) by defining the postintervention SDE resulting from an intervention in an SDE. We show that under Lipschitz conditions, the solution to the postintervention SDE is equal to a uniform limit in probability of postintervention structural equation models based on the Euler scheme of the original SDE, thus relating our definition to mainstream causal concepts. We prove that when the driving noise in the SDE is a Lévy process, the postintervention distribution is identifiable from the generator of the SDE.

References in corpus (4)

• Estimating high-dimensional intervention effects from observational data
• On the Identifiability of the Post-Nonlinear Causal Model
• Identifiability of Gaussian structural equation models with equal error variances
• From Ordinary Differential Equations to Structural Causal Models: the deterministic case

Cited by in corpus (8)

• From Ordinary Differential Equations to Structural Causal Models: the deterministic case
• Markov equivalence of marginalized local independence graphs
• From Deterministic ODEs to Dynamic Structural Causal Models
• Beyond Structural Causal Models: Causal Constraints Models
• Graphical modeling of stochastic processes driven by correlated errors
• Dynamic Causal Bayesian Optimization
• Graphical continuous Lyapunov models
• Identifying Causal Structure in Dynamical Systems