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Causal interpretation of stochastic differential equations. (English) Zbl 1307.60080
Summary: 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.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G51 Processes with independent increments; Lévy processes
62A01 Foundations and philosophical topics in statistics
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