@inbook{80b3f42ed0ba46a4a621a16329d1c2b2,
title = "Stochastic Differential Equations Driven by Loops",
abstract = "We study stochastic differential equations of the type (formula presented) where (Ms)0 ≤ s ≤ T is a semimartingale generating a loop in the free Carnot group of step N and show how the properties of the random variable XT x are closely related to the Lie subalgebra generated by the commutators of the Vi{\textquoteright}s with length greater than N + 1. It is furthermore shown that if f is a smooth function, then (formula presented) is a second order operator related to the Vi′s.",
keywords = "Brownian loops, Carnot groups, Chen development, Holonomy operator, H{\"o}rmander{\textquoteright}s type theorems",
author = "Fabrice Baudoin",
note = "Publisher Copyright: {\textcopyright} 2015, Springer International Publishing Switzerland.",
year = "2015",
doi = "10.1007/978-3-319-13984-5_3",
language = "English",
series = "Progress in Probability",
publisher = "Birkhauser",
pages = "59--80",
booktitle = "Progress in Probability",
}