In this section
@article{Arnaudon:2017:10.1016/j.crme.2018.01.003,
author = {Arnaudon, A and Ganaba, N and Holm, DD},
doi = {10.1016/j.crme.2018.01.003},
journal = {Comptes Rendus. Mécanique},
pages = {279--290},
title = {The stochastic energy-Casimir method},
url = {http://dx.doi.org/10.1016/j.crme.2018.01.003},
volume = {346},
year = {2017}
}
TY - JOUR
AB - <jats:p id="sp0020">In this paper, we extend the energy-Casimir stability method for deterministic Lie–Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems.</jats:p>
AU - Arnaudon,A
AU - Ganaba,N
AU - Holm,DD
DO - 10.1016/j.crme.2018.01.003
EP - 290
PY - 2017///
SN - 1631-0721
SP - 279
TI - The stochastic energy-Casimir method
T2 - Comptes Rendus. Mécanique
UR - http://dx.doi.org/10.1016/j.crme.2018.01.003
UR - https://doi.org/10.1016/j.crme.2018.01.003
VL - 346
ER -