Electronic Journal of Probability

Causal interpretation of stochastic differential equations

Niels Hansen and Alexander Sokol

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 100, 24 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065742

Digital Object Identifier
doi:10.1214/EJP.v19-2891

Mathematical Reviews number (MathSciNet)
MR3275852

Zentralblatt MATH identifier
1307.60080

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 62A01: Foundations and philosophical topics

Keywords
Stochastic diferential equation Causality Structural equation model Identifiability Levy process Weak conditional local independence

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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