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arXiv · 2504.04379

On the averaging theorems for stochastic perturbation of conservative linear systems

Jing Guo·Sergei Kuksin·Zhenxin Liu
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Abstract

For stochastic perturbations of linear systems with non-zero pure imaginary spectrum we discuss the averaging theorems in terms of the slow-fast action-angle variables and in the sense of Krylov-Bogoliubov. Then we show that if the diffusion matrix of the perturbation is uniformly elliptic, then in all cases the averaged dynamics does not depend on a hamiltonian part of the perturbation.

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Jing Guo, Sergei Kuksin, Zhenxin Liu. 2025-04-06. On the averaging theorems for stochastic perturbation of conservative linear systems. https://arxiv.org/abs/2504.04379

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