Causal interpretation of stochastic differential equations

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Causal interpretation of stochastic differential equations. / Sokol, Alexander; Hansen, Niels Richard.

In: Electronic Journal of Probability, Vol. 19, 100, 26.10.2014, p. 1-24.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Sokol, A & Hansen, NR 2014, 'Causal interpretation of stochastic differential equations', Electronic Journal of Probability, vol. 19, 100, pp. 1-24. https://doi.org/10.1214/EJP.v19-2891

APA

Sokol, A., & Hansen, N. R. (2014). Causal interpretation of stochastic differential equations. Electronic Journal of Probability, 19, 1-24. [100]. https://doi.org/10.1214/EJP.v19-2891

Vancouver

Sokol A, Hansen NR. Causal interpretation of stochastic differential equations. Electronic Journal of Probability. 2014 Oct 26;19:1-24. 100. https://doi.org/10.1214/EJP.v19-2891

Author

Sokol, Alexander ; Hansen, Niels Richard. / Causal interpretation of stochastic differential equations. In: Electronic Journal of Probability. 2014 ; Vol. 19. pp. 1-24.

Bibtex

@article{1347bebc54aa4f3ba6f2d120326e3757,
title = "Causal interpretation of stochastic differential equations",
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 L{\'e}vy process, the postintervention distribution is identifiable from the generator of the SDE.",
keywords = "Stochastic differential equation, Causality, Structural equation model, Identifiability, Levy process, Weak conditional local independence",
author = "Alexander Sokol and Hansen, {Niels Richard}",
year = "2014",
month = oct,
day = "26",
doi = "10.1214/EJP.v19-2891",
language = "English",
volume = "19",
pages = "1--24",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - Causal interpretation of stochastic differential equations

AU - Sokol, Alexander

AU - Hansen, Niels Richard

PY - 2014/10/26

Y1 - 2014/10/26

N2 - 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.

AB - 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.

KW - Stochastic differential equation

KW - Causality

KW - Structural equation model

KW - Identifiability

KW - Levy process

KW - Weak conditional local independence

U2 - 10.1214/EJP.v19-2891

DO - 10.1214/EJP.v19-2891

M3 - Journal article

VL - 19

SP - 1

EP - 24

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

M1 - 100

ER -

ID: 135496308