Variational Principles on Geometric Rough Paths and the Lévy Area Correction
arXiv:2208.13706 · doi:10.1137/22M1522164
Abstract
In this paper, we describe two effects of the Lévy area correction on the invariant measure of stochastic rigid body dynamics on geometric rough paths. From the viewpoint of dynamics, the Lévy area correction introduces an additional deterministic torque into the rigid body motion equation on geometric rough paths. When the dynamics is driven by coloured noise, and for rigid body dynamics with double-bracket dissipation, theoretical and numerical results show that this additional deterministic torque shifts the centre of the probability distribution function by shifting the Hamiltonian function in the exponent of the Gibbsian invariant measure.
arXiv comment39 pages, 9 figures, 3rd version, comments welcome
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