论文标题
与杆振动相关的假发孔
Pseudoprocesses related to higher-order equations of vibrations of rods
论文作者
论文摘要
在本文中，我们研究了菲涅耳假述，其签名的度量密度是杆振动方程的高阶扩展的解决方案。我们还研究了与Riesz运营商相关的假源的空间分数扩展。量度密度以广义通风函数为代表，这些功能包括经典的通风函数作为特定情况。我们证明，使用独立的稳定下属的菲涅耳假述时间变化会产生真正的随机过程。特别是，如果以适当的方式选择下属的指数，则随时间变化的伪源剂在分布方面与稳定过程的混合物相同。讨论了Cauchy分布的混合物的情况，我们表明对称混合物可以是单峰或双峰的，而不对称混合物的概率密度函数可能具有拐点。
In this paper we study Fresnel pseudoprocesses whose signed measure density is a solution to a higher-order extension of the equation of vibrations of rods. We also investigate space-fractional extensions of the pseudoprocesses related to the Riesz operator. The measure density is represented in terms of generalized Airy functions which include the classical Airy function as a particular case. We prove that the Fresnel pseudoprocess time-changed with an independent stable subordinator produces genuine stochastic processes. In particular, if the exponent of the subordinator is chosen in a suitable way, the time-changed pseudoprocess is identical in distribution to a mixture of stable processes. The case of a mixture of Cauchy distributions is discussed and we show that the symmetric mixture can be either unimodal or bimodal, while the probability density function of an asymmetric mixture can possibly have an inflection point.
