扩散运动中的重尾目标和（ab）正态渐近性
Heavy-tailed targets and (ab)normal asymptotics in diffusive motion
摘要：
我们研究了在约束条件下，具有共同重尾渐近（目标）概率密度函数的范式跳跃型和连续过程的概率密度函数的时间行为。也就是说，我们已经证明，在适当的限制条件下，普通的福克-普朗克方程可以在其长时间渐近性中产生非高斯重尾分布（例如柯西分布或更一般的Lévy稳定分布）。对于扩散型过程，我们的主要重点是他们的瞬态制度，特别是交叉功能，当最初无限数量的PDF时刻下降到几个或根本没有。方差的时间依赖性（如果存在），$\sim t^γ$与$0<γ<2$，原则上可以解释为在限制条件下的亚扩散、正常扩散或超扩散行为的特征;指数$γ$一般在相当长的时间段内定义良好。然而，由于驱动程序和/或外部电位的适当选择，没有任何通用时间速率等级的指示。
英文摘要：
We investigate temporal behavior of probability density functions (pdfs) of paradigmatic jump-type and continuous processes that, under confining regimes, share common heavy-tailed asymptotic (target) pdfs. Namely, we have shown that under suitable confinement conditions, the ordinary Fokker-Planck equation may generate non-Gaussian heavy-tailed pdfs (like e.g. Cauchy or more general Lévy stable distribution) in its long time asymptotics. For diffusion-type processes, our main focus is on their transient regimes and specifically the crossover features, when initially infinite number of the pdf moments drops down to a few or none at all. The time-dependence of the variance (if in existence), $\sim t^γ$ with $0<γ<2$, in principle may be interpreted as a signature of sub-, normal or super-diffusive behavior under confining conditions; the exponent $γ$ is generically well defined in substantial periods of time. However, there is no indication of any universal time rate hierarchy, due to a proper choice of the driver and/or external potential.
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