Higher-Order Laplace Equations and Hyper-Cauchy Distributions

Enzo Orsingher () and Mirko D’Ovidio ()
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Enzo Orsingher: Sapienza University of Rome
Mirko D’Ovidio: Sapienza University of Rome

Journal of Theoretical Probability, 2015, vol. 28, issue 1, 92-118

Abstract: 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 stable distributions which produce asymmetric Cauchy densities in the odd-order case. 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.

Keywords: Pseudo-processes; Stable processes; Cauchy processes; Higher-order Laplace equations; Airy functions; Modified Bessel functions; 60G52; 35C05 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0480-5

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