Dimension dependent properties of subdiffusions in damping force fields from an inference perspective
Dimension dependent properties of subdiffusions in damping force fields from an inference perspective
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DOI：
10.1088/1402-4896/aca3d8
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发表时间：
2022-12
期刊：
影响因子：
2.9
通讯作者：
Yue He;Ray Kawai
中科院分区：
文献类型：
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作者：
Yue He;Ray Kawai
研究了分数阶Fokker-Planck方程在阻尼力作用下的维数依赖性质。我们揭示了各种令人惊讶的性质，其解决方案通过相应的概率密度函数的透镜的非线性均方位移，如存在性，奇异性，正则性，模态，平稳性和二阶结构，这在很大程度上取决于尺寸和随机时钟。考虑到轨迹信息通常是从多维系统中收集的，当偏离众所周知的单变量框架时，所发现的事实有可能作为推理、模型识别和预测的关键基础和警报发挥重要作用。
We investigate the fractional Fokker-Planck equation subject to a damping force with an emphasis on its dimension dependent properties. We reveal a variety of surprising properties of its solution through the lens of the probability density function of the corresponding stochastic process with nonlinear mean square displacements, such as existence, singularity, regularity, modality, stationarity and second-order structure, which are largely dependent on the dimension and the random clock. Taking into account that the trajectory information is most often collected from multidimensional systems, the discovered facts have the potential to play important roles as key foundations and alerts for inference, model identification and prediction, when departing from the well-understood univariate framework.