Goldstein-Kac telegraph processes with random speeds: Path probabilities, likelihoods, and reported Lévy flights.
Goldstein-Kac telegraph processes with random speeds: Path probabilities, likelihoods, and reported Lévy flights.
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Goldstein-Kac 电报以随机速度进行处理：路径概率、可能性和报告的 Lévy 航班。
DOI：
10.1103/physreve.91.042115
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发表时间：
2015
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影响因子：
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通讯作者：
Sim A
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作者：
Sim A
Goldstein-Kac 电报过程描述了粒子以恒定速度进行方向随机变化的一维运动。尽管它与许多现实世界的现象相似，但每个粒子的空间分布的奇异性质排除了从数据中对这种随机游走模型进行任何后验验证的可能性。在这里，我们证明，通过简单地考虑随机速度，弹道项被正则化，并且扩散分量可以通过无迹变换很好地近似。其结果是对整个粒子路径概率以及该广义电报过程的参数似然进行计算高效且稳健的评估。我们证明了在这种模型下的种群扩散如何导致非高斯渐近空间分布，从而模仿 Lévy 步行者集合的行为。
The Goldstein-Kac telegraph process describes the one-dimensional motion of particles with constant speed undergoing random changes in direction. Despite its resemblance to numerous real-world phenomena, the singular nature of the resultant spatial distribution of each particle precludes the possibility of anya posterioriempirical validation of this random-walk model from data. Here we show that by simply allowing for random speeds, the ballistic terms are regularized and that the diffusion component can be well-approximated via the unscented transform. The result is a computationally efficient yet robust evaluation of the full particle path probabilities and, hence, the parameter likelihoods of this generalized telegraph process. We demonstrate how a population diffusing under such a model can lead to non-Gaussian asymptotic spatial distributions, thereby mimicking the behavior of an ensemble of Lévy walkers.