Intervention in Ornstein-Uhlenbeck SDEs
Probability
2014-10-28 v1
Abstract
We introduce a notion of intervention for stochastic differential equations and a corresponding causal interpretation. For the case of the Ornstein-Uhlenbeck SDE, we show that the SDE resulting from a simple type of intervention again is an Ornstein-Uhlenbeck SDE. We discuss criteria for the existence of a stationary distribution for the solution to the intervened SDE. We illustrate the effect of interventions by calculating the mean and variance in the stationary distribution of an intervened process in a particularly simple case.
Cite
@article{arxiv.1308.2152,
title = {Intervention in Ornstein-Uhlenbeck SDEs},
author = {Alexander Sokol},
journal= {arXiv preprint arXiv:1308.2152},
year = {2014}
}
Comments
Extended version of article to be presented at the 18th EYSM