Cusping, transport and variance of solutions to generalized Fokker–Planck equations
Cusping, transport and variance of solutions to generalized Fokker–Planck equations
复制标题
广义福克-普朗克方程解的尖点、输运和方差
DOI：
10.1088/1751-8121/aa6f67
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Ray Kawai
中科院分区：
文献类型：
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作者：
Sean Carnaffan;Ray Kawai
我们通过反常扩散过程的概率密度函数的视角来研究广义福克-普朗克方程解的性质。特别是，我们在广义福克-普朗克方程的随机表示框架内，根据尖点、行波行为和方差来检查解。我们对由稳定、调节稳定和伽玛从属子的逆驱动的异常扩散的情况进行了分析，证明了改变底层异常扩散模型中等待时间分布的影响。我们还分析了底层异常扩散在父进程中包含 Lévy 跳跃分量的情况，以及扩散过程被非逆 Lévy 从属器时间改变的情况。总的来说，我们提出了四个标准的组合，作为异常扩散系统物理实验的模型选择、统计推断和预测的理论基础。我们讨论了物理实验中可能的应用，包括参考具体示例，模型错误分类的可能性以及如何使用我们的四个标准的组合来克服这个问题。
We study properties of solutions to generalized Fokker–Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker–Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.
DOI：
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发表时间：
2010
期刊：
影响因子：
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作者：
Neoro;H;MAXI Team;Shigeo Kusuoka
通讯作者：
Shigeo Kusuoka