高阶Laplace方程与超柯西分布
Higher-order Laplace equations and hyper-Cauchy distributions
摘要：
在本文中，我们介绍了新的分布，这是高阶拉普拉斯方程的解决方案。证明了它们的密度可以通过柯西分布的折叠和对称化得到。另一类与高阶Laplace方程有关的概率律是通过将伪过程与正偏的柯西分布组合而得到的，这些分布在奇数阶情况下产生非对称的柯西密度.特别注意三阶Laplace方程，其中的柯西分布和Airy函数之间的联系得到和分析。
英文摘要：
In this paper we introduce new distributions which are solutions of higher-order Laplace equations. It is proved that their densities can be obtained by folding and symmetrizing Cauchy distributions. Another class of probability laws related to higher-order Laplace equations is obtained by composing pseudo-processes with positively-skewed Cauchy distributions which produce asymmetric Cauchy densities in the odd-order case. A special attention is devoted to the third-order Laplace equation where the connection between the Cauchy distribution and the Airy functions is obtained and analyzed.
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