The Stochastic Energy-Casimir Method
File(s)
Working paper
Author(s)
Arnaudon, Alexis
Ganaba, Nader
Holm, Darryl
Type
Working Paper
Abstract
In this paper, we extend the energy-Casimir stability method for
deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions
for the stability in probability of stochastic dynamical systems with
symmetries and multiplicative noise. 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 of this
extension is that stable deterministic equilibria remain stable in probability
up to a certain stopping time which depends on the amplitude of the noise for
finite dimensional systems and on the amplitude the spatial derivative of the
noise for infinite dimensional systems.
deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions
for the stability in probability of stochastic dynamical systems with
symmetries and multiplicative noise. 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 of this
extension is that stable deterministic equilibria remain stable in probability
up to a certain stopping time which depends on the amplitude of the noise for
finite dimensional systems and on the amplitude the spatial derivative of the
noise for infinite dimensional systems.
Date Issued
2018-04-01
Date Acceptance
2018-01-18
Citation
Comptes Rendus Mécanique
ISSN
1631-0721
Publisher
Elsevier Masson
Journal / Book Title
Comptes Rendus Mécanique
Copyright Statement
© 2017 The Author(s)
Identifier
http://arxiv.org/abs/1702.03899v1
Subjects
math.DS
math.DS