Data di Pubblicazione:
2006
Citazione:
Minimal cyclic random motion in R-n and hyper-Bessel functions / A. Lachal, S. Leorato, E. Orsingher. - In: ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. - ISSN 0246-0203. - 42:6(2006), pp. 753-772.
Abstract:
We obtain the explicit distribution of the position of a particle performing a cyclic, minimal, random motion with constant velocity c in Rn. The n + 1 possible directions of motion as well as the support of the distribution form a regular hyperpolyhedron (the first one having constant sides and the other expanding with time t), the geometrical features of which are here investigated. The distribution is obtained by using order statistics and is expressed in terms of hyper-Bessel functions of order n + 1. These distributions are proved to be connected with (n + 1)th order p.d.e. which can be reduced to Bessel equations of higher order. Some properties of the distributions obtained are examined. This research has been inspired by a conjecture formulated in Orsingher and Sommella [E. Orsingher, A.M. Sommella, A cyclic random motion in R3 with four directions and finite velocity, Stochastics Stochastics Rep. 76 (2) (2004) 113-133] which is here proved to be false.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
cyclic random motions; hyper-Bessel functions; (n+1)th order partial differential equations; order statistics; hyperpolyhedron
Elenco autori:
A. Lachal, S. Leorato, E. Orsingher
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