Abstract
We study stochastic differential equations of the type
where (M s )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 X T x are closely related to the Lie subalgebra generated by the commutators of the V i ’s with length greater than N + 1. It is furthermore shown that if f is a smooth function, then
where \(\Delta _{N}\) is a second order operator related to the V i ′s.
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Baudoin, F. (2015). Stochastic Differential Equations Driven by Loops. In: Mena, R., Pardo, J., Rivero, V., Uribe Bravo, G. (eds) XI Symposium on Probability and Stochastic Processes. Progress in Probability, vol 69. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-13984-5_3
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DOI: https://doi.org/10.1007/978-3-319-13984-5_3
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