Motions with finite velocity analyzed with order statistics and differential equations
TLDR
In this paper, the explicit distribution of the position of randomly moving particles on the line and in the plane (with different velocities taken cyclically) by means of order statistics and by studying suitable problems of differential equations is derived.Abstract:
The aim of this paper is to derive the explicit distribution of the position of randomly moving particles on the line and in the plane (with different velocities taken cyclically) by means of order statistics and by studying suitable problems of differential equations. The two approaches are compared when both are applicable (case of the telegraph process). In some specific cases (alternating motions with skipping) it is possible to use the order statistics approach also to solve the equations governing the distribution. Finally, the approach based on order statistics is also applied in order to obtain the distribution of the position in the case of planar motion with three velocities conditioned on the number of changes of directions recorded.read more
Citations
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On the asymmetric telegraph processes
Oscar López,Nikita Ratanov +1 more
TL;DR: In this article, the authors studied the one-dimensional random motion X = X(t), t ≥ 0, which takes two different velocities with two different alternating intensities, and obtained closed-form formulae for the density functions of X and for the moments of any order.
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Flying randomly in Rd with Dirichlet displacements
TL;DR: In this article, the authors derived the probability distributions of random flights in R d, d ≥ 2 with Dirichlet-distributed displacements and uniformly distributed orientation by inverting the characteristic functions of the position X ¯ d ( t ), t > 0.
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Fractional Klein–Gordon Equations and Related Stochastic Processes
TL;DR: In this paper, the fractional hyper-Bessel operator was converted into the Erdelyi-Kober integral operator and the distribution of fractional Klein-Gordon equations was analyzed.
Posted Content
Random flights related to the Euler-Poisson-Darboux equation
Roberto Garra,Enzo Orsingher +1 more
TL;DR: In this article, the analysis of random motions on the line and in the space R^d (d > 1) performed at finite velocity and governed by a non-homogeneous Poisson process with rate λ(t) is presented.
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Large deviation principles for telegraph processes
TL;DR: In this article, the authors present large deviation results for some telegraph random motions, and compare the rate function with the one obtained for the non-conditional distributions for the classical case.
References
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Properties of the telegrapher's random process with or without a trap
S.K. Foong,S. Kanno +1 more
TL;DR: In this article, the properties of the telegrapher random process which is a Poissonian random walk on a straight line are studied in detail in probabilistic terms.
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Bessel functions of third order and the distribution of cyclic planar motions with three directions
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.
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Bose-Einstein-type statistics, order statistics and planar random motions with three directions
Samantha Leorato,Enzo Orsingher +1 more
TL;DR: In this article, the authors studied different types of planar random motions with three directions and derived the explicit distribution of the position of the particle, by using an approach based on order statistics, and proved that the densities obtained are solutions of the partial differential equations governing the processes.
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Markovian random evolution in Rn
TL;DR: In this paper, the authors studied minimal random evolutions and their applications to the solution of the telegraph equation of high degree, which is a generalization of the one-dimensional Kac model.