Electronic Journal of Probability
- Electron. J. Probab.
- Volume 19 (2014), paper no. 100, 24 pp.
Causal interpretation of stochastic differential equations
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.
Electron. J. Probab., Volume 19 (2014), paper no. 100, 24 pp.
Accepted: 26 October 2014
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 62A01: Foundations and philosophical topics
This work is licensed under a Creative Commons Attribution 3.0 License.
Hansen, Niels; Sokol, Alexander. Causal interpretation of stochastic differential equations. Electron. J. Probab. 19 (2014), paper no. 100, 24 pp. doi:10.1214/EJP.v19-2891. https://projecteuclid.org/euclid.ejp/1465065742