Higher-order Laplace equations and hyper-Cauchy distributions

Details Higher-order Laplace equations and hyper-Cauchy distributions Higher-order Laplace equations and hyper-Cauchy distributions

2011-12-30

arxiv.org/abs/1201.0141v1

Mathematics

Probability

20 pages; 5 figures

Scientific paper

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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