Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion
Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion
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DOI：
10.1007/s10955-020-02485-4
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发表时间：
2019-05
影响因子：
1.6
通讯作者：
Katharina Eichinger;C. Kuehn;A. Neamţu
中科院分区：
文献类型：
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作者：
Katharina Eichinger;C. Kuehn;A. Neamţu
我们分析了加性分数噪声与赫斯特参数对快慢系统的影响。我们的策略基于样本路径估计，类似于伯格伦德和根茨在布朗运动案例中的方法。然而，分数布朗运动的设置不允许我们使用具有布朗运动的快慢系统的鞅方法。我们彻底研究了确定性系统允许一致双曲稳定慢流形的情况。在这种设置中，我们提供了一个针对系统的快慢结构量身定制的邻域，其中包含高概率的过程。我们通过提供系统离开该邻域的概率的指数误差估计来证明这一断言。我们还在气候建模中的一个例子中说明了我们的结果，其中时间相关的噪声过程最近变得更加相关。
We analyze the effect of additive fractional noise with Hurst parameteron fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet, the setting of fractional Brownian motion does not allow us to use the martingale methods from fast-slow systems with Brownian motion. We thoroughly investigate the case where the deterministic system permits a uniformly hyperbolic stable slow manifold. In this setting, we provide a neighborhood, tailored to the fast-slow structure of the system, that contains the process with high probability. We prove this assertion by providing exponential error estimates on the probability that the system leaves this neighborhood. We also illustrate our results in an example arising in climate modeling, where time-correlated noise processes have become of greater relevance recently.