Higher-order Laplace equations and hyper-Cauchy distributions

Enzo Orsingher; Mirko D'Ovidio

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arXiv · 1201.0141

Higher-order Laplace equations and hyper-Cauchy distributions

Enzo Orsingher·Mirko D'Ovidio

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Abstract

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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BibTeX RIS

Enzo Orsingher, Mirko D'Ovidio. 2013-02-05. Higher-order Laplace equations and hyper-Cauchy distributions. https://arxiv.org/abs/1201.0141

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