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Higher-Order Laplace Equations and Hyper-Cauchy Distributions

Author

Listed:
  • Enzo Orsingher

    (Sapienza University of Rome)

  • Mirko D’Ovidio

    (Sapienza University of Rome)

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.

Suggested Citation

  • Enzo Orsingher & Mirko D’Ovidio, 2015. "Higher-Order Laplace Equations and Hyper-Cauchy Distributions," Journal of Theoretical Probability, Springer, vol. 28(1), pages 92-118, March.
    • Handle: RePEc:spr:jotpro:v:28:y:2015:i:1:d:10.1007_s10959-013-0480-5
    DOI: 10.1007/s10959-013-0480-5
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    References listed on IDEAS

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    1. Mirko D’Ovidio & Enzo Orsingher, 2011. "Composition of Processes and Related Partial Differential Equations," Journal of Theoretical Probability, Springer, vol. 24(2), pages 342-375, June.
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