特殊极限情形下Sine-Wiener噪声及其诱导逃逸的性质研究$D \to \infty$
Investigation on the properties of Sine-Wiener noise and its induced escape in the particular limit case $D \to \infty$
摘要：
正弦-维纳噪声由于其有界性，在实际随机建模中得到越来越多的应用。然而，SW噪声的许多特征仍然未被探索。本文首先研究了当SW噪声中的参数$D$趋于无穷大时SW噪声的性质及其积分过程。研究发现，虽然SW噪声的分布与高斯白噪声有很大的不同，但SW噪声的积分过程与Wiener过程有许多相似之处。受Wiener过程用扩散系数表示高斯噪声强度的启发，提出了一个量化SW噪声强度的方法。然后，我们将SW噪声应用到一维双势阱系统和Maier-Stein系统中，研究了它们的逃逸行为。一个更有趣的结果是观察到的平均第一出口时间也遵循著名的阿克里先乌斯定律的情况下的高斯噪声，和准势和出口位置分布是非常接近的高斯噪声的结果。
英文摘要：
Sine-Wiener noise is increasingly adopted in realistic stochastic modeling for its bounded nature. However, many features of the SW noise are still unexplored. In this paper, firstly, the properties of the SW noise and its integral process are explored as the parameter $D$ in the SW noise tends to infinite. It is found that although the distribution of the SW noise is quite different from Gaussian white noise, the integral process of the SW noise shows many similarities with the Wiener process. Inspired by the Wiener process, which uses the diffusion coefficient to denote the intensity of the Gaussian noise, a quantity is put forward to characterize the SW noise's intensity. Then we apply the SW noise to a one-dimensional double-well potential system and the Maier-Stein system to investigate the escape behaviors. A more interesting result is observed that the mean first exit time also follows the well-known Arrhenius law as in the case of the Gaussian noise, and the quasi-potential and the exit location distributions are very close to the results of the Gaussian noise.
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