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Showing papers by "Enzo Orsingher published in 2002"


Journal ArticleDOI
TL;DR: In this paper, the exact distribution of a cyclic planar motion with three directions is explicitly derived in terms of Bessel functions of order three (suitably combined) and the absolutely continuous part of the distribution is proved to satisfy suitable boundary conditions and some of its properties are analyzed.
Abstract: The exact distribution of a cyclic planar motion with three directions is explicitly derived in terms of Bessel functions of order three (suitably combined). The absolutely continuous part of the distribution is proved to satisfy suitable boundary conditions and some of its properties are analyzed. The transformations converting the governing equations of order three is presented and its solutions (used here) derived by applying the Frobenius method.

21 citations


Journal ArticleDOI
TL;DR: In this paper, a four-direction planar random motion with finite velocity and with possible reflections at Poisson-paced events is examined, and the equations governing the distributions within the diffusion set are obtained.
Abstract: A four-direction planar random motion with finite velocity and with possible reflections at Poisson-paced events is examined. We obtain the equations governing the distributions within the diffusion set $Q_t$ and the equations directing the singular components of the distributions. The distributions on the edge of $Q_t$ and its diagonals are explicitly obtained.

13 citations


Journal ArticleDOI
TL;DR: In this paper, the authors considered planar random motions with four directions and four different speeds, switching at Poisson paced times, and obtained the explicit distribution of the position (X(t),Y(t)), t>0 in all its components (the discrete one, lying on the edge and the absolutely continuous one, concentrated inside Qt).
Abstract: In this paper we consider planar random motions with four directions and four different speeds, switching at Poisson paced times. We are able to obtain, in some cases, the explicit distribution of the position (X(t),Y(t)), t>0 in all its components (the discrete one, lying on the edge ∂Qt of the probability support Qt, as well as the absolutely continuous one, concentrated inside Qt).

11 citations