Koopman Operator Spectrum for Random Dynamical Systems

被引：35
作者：
Crnjaric-Zic, Nelida [1 ]
Macesic, Senka [1 ]
Mezic, Igor [2 ]
机构：
[1] Univ Rijeka, Fac Engn, Vukovarska 58, Rijeka 51000, Croatia
[2] Univ Calif Santa Barbara, Fac Mech Engn & Math, Santa Barbara, CA 93106 USA
来源：
JOURNAL OF NONLINEAR SCIENCE | 2020年 / 30卷 / 05期
关键词：
Stochastic Koopman operator; Random dynamical systems; Stochastic differential equations; Dynamic mode decomposition; MODE DECOMPOSITION; REDUCTION;
D O I：
10.1007/s00332-019-09582-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the Koopman operator associated with the discrete and the continuous-time random dynamical system (RDS). We provide results that characterize the spectrum and the eigenfunctions of the stochastic Koopman operator associated with different types of linear RDS. Then we consider the RDS for which the associated Koopman operator family is a semigroup, especially those for which the generator can be determined. We define a stochastic Hankel-DMD algorithm for numerical approximations of the spectral objects (eigenvalues, eigenfunctions) of the stochastic Koopman operator and prove its convergence. We apply the methodology to a variety of examples, revealing objects in spectral expansions of the stochastic Koopman operator and enabling model reduction.
引用
收藏
页码：2007 / 2056
页数：50
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