Causal interpretation of stochastic differential equations

Niels Richard Hansen (University of Copenhagen)
Alexander Sokol (University of Copenhagen)

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.

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Pages: 1-24

Publication Date: October 26, 2014

DOI: 10.1214/EJP.v19-2891

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