Decomposition of stochastic flow and an averaging principle for slow perturbations

被引:2
作者
Ledesma, Diego Sebastian [1 ]
Borges da Silva, Fabiano [2 ]
机构
[1] Univ Estadual Campinas, Campinas, SP, Brazil
[2] Univ Estadual Paulista UNESP, Bauru, SP, Brazil
来源
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL | 2020年 / 35卷 / 04期
基金
巴西圣保罗研究基金会;
关键词
Averaging principle; decomposition of stochastic flow; slow perturbations; diffusion;
D O I
10.1080/14689367.2020.1769031
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work we use the stochastic flow decomposition technique to get components that represent the dynamics of the slow and fast motion of a stochastic differential equation with a random perturbation. Assuming a Lipschitz condition for vector fields and an average principle we get an approximation for the slow motion. To obtain the estimate for the rate of convergence we use a distance function which is defined in terms of the height functions associated to an isometric embedding of the manifold into the Euclidean space. This metric is topologically equivalent to the Riemannian distance given by the infimum of the lengths of all admissible curves between two points and works well with stochastic calculation tools. Finally, we get an estimate for the approximation between the solution of perturbed system and the original process provided by the unperturbed.
引用
收藏
页码:625 / 654
页数:30
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