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2014 Causal interpretation of stochastic differential equations
Niels Hansen, Alexander Sokol
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Electron. J. Probab. 19: 1-24 (2014). DOI: 10.1214/EJP.v19-2891

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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Niels Hansen. Alexander Sokol. "Causal interpretation of stochastic differential equations." Electron. J. Probab. 19 1 - 24, 2014. https://doi.org/10.1214/EJP.v19-2891

Information

Accepted: 26 October 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1307.60080
MathSciNet: MR3275852
Digital Object Identifier: 10.1214/EJP.v19-2891

Subjects:
Primary: 60H10
Secondary: 62A01

JOURNAL ARTICLE
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Vol.19 • 2014
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