On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
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DOI：
10.1007/s10955-016-1605-x
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发表时间：
2015-12
影响因子：
1.6
通讯作者：
N. Glatt-Holtz;Jonathan C. Mattingly;Geordie Richards
中科院分区：
文献类型：
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作者：
N. Glatt-Holtz;Jonathan C. Mattingly;Geordie Richards
我们说明了如何渐近耦合的概念提供了一个灵活和直观的框架，证明各种随机偏微分方程的确定性对应具有有限数量的确定模式的不变措施的唯一性。展示抛物型和双曲型结构的例子进行了详细研究。在后一种情况下，我们也提出了一个简单的框架，建立不变的措施时，通常的方法依赖于Krylov-Bogolyubov程序和紧凑性失败的存在。
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart possesses a finite number of determining modes. Examples exhibiting parabolic and hyperbolic structure are studied in detail. In the later situation we also present a simple framework for establishing the existence of invariant measures when the usual approach relying on the Krylov–Bogolyubov procedure and compactness fails.