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Causal interpretation of stochastic differential equations

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1.	Title	Title of document	Causal interpretation of stochastic differential equations
2.	Creator	Author's name, affiliation, country	Niels Richard Hansen; University of Copenhagen; Denmark
2.	Creator	Author's name, affiliation, country	Alexander Sokol; University of Copenhagen; Denmark
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Stochastic diferential equation; Causality; Structural equation model; Identifiability; Levy process; Weak conditional local independence
3.	Subject	Subject classification	60H10; 62A01
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2014-10-26
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2891
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-2891
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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