论文标题
高斯过程的单个设备光谱密度的频率相关性
Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes
论文作者
论文摘要
我们研究了几个高斯随机过程，即布朗运动，Ornstein-uhlenbeck过程，Brownian Gyrator模型和分数Brownian Motion，作为频率$ω$ $的函数$ chant funcy $ funcy f f f flosever，我们研究了几个高斯随机过程，即布朗斯坦 - uhlenbeck的过程，频率$ω$ $ $ function $ c。我们特别评估了$ s（ω，\ mathcal {t}）$的方差和频率相关性，以$ω$的不同值。我们表明，这些特性对不同的物理病例表现出不同的行为，因此可以用作敏感的探针区分不同种类的随机运动。这些结果可能在分析实验数据中非常有用。
We investigate the stochastic behavior of the single-trajectory spectral density $S(ω,\mathcal{T})$ of several Gaussian stochastic processes, i.e., Brownian motion, the Ornstein-Uhlenbeck process, the Brownian gyrator model and fractional Brownian motion, as a function of the frequency $ω$ and the observation time $\mathcal{T}$. We evaluate in particular the variance and the frequency-frequency correlation of $S(ω,\mathcal{T})$ for different values of $ω$. We show that these properties exhibit different behaviors for different physical cases and can therefore be used as a sensitive probe discriminating between different kinds of random motion. These results may prove quite useful in the analysis of experimental data.
