We consider in this work a model conservative system subject to dissipation and Gaussian-type stochastic perturbations. The original conservative system possesses a continuous set of steady states and is thus degenerate. We characterize the long-time limit of our model system as the perturbation parameter tends to zero. The degeneracy in our model system carries features found in some partial differential equations related, for example, to turbulence problems.

中文翻译：

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具有退化的扰动保守系统的长期行为

我们在这项工作中考虑了一个受耗散和高斯型随机扰动影响的模型保守系统。原来的保守系统拥有一组连续的稳态，因此是退化的。我们将模型系统的长时间限制表征为扰动参数趋于零。我们模型系统中的简并性带有在一些与湍流问题相关的偏微分方程中发现的特征。