The stochastic energy-Casimir method

被引：8

作者：

Arnaudon, Alexis ^{[1
]}

Ganaba, Nader ^{[1
]}

Holm, Darryl D. ^{[1
]}

机构：

[1] Imperial Coll, Dept Math, London SW7 2AZ, England

来源：

COMPTES RENDUS MECANIQUE | 2018年 / 346卷 / 04期

基金：

欧洲研究理事会; 英国工程与自然科学研究理事会;

关键词：

Stochastic geometric mechanics; Energy-Casimir method; Stochastic stability; DIRAC STRUCTURES;

D O I：

10.1016/j.crme.2018.01.003

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

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. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：279 / 290

页数：12

共 24 条

[1]

[Anonymous], 1966, IZV VUZ MAT+

[2] Noise and Dissipation on Coadjoint Orbits [J].