Planar random motions with drift
Enzo Orsingher,Nikita Ratanov +1 more
TLDR
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).read more
Citations
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Cyclic random motions in $\mathbb{R}^d$-space with $n$ directions
TL;DR: In this article, the authors studied the probability distribution of the location of a cyclic random motion in a polyhedron and showed that the distribution is made up of two components: a singular component (corresponding to the beginning of the travel of the particle) and an absolutely continuous component.
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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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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.
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Certain functionals of squared telegraph processes
TL;DR: In this article, the stochastic process defined as the square of the (integrated) symmetric telegraph process is investigated and its probability law and a closed form expression of the moment g are obtained.
CYCLIC RANDOM MOTIONS IN R d -SPACE WITH n DIRECTIONS
TL;DR: In this article, the probability distribution of the location of a particle performing a cyclic random motion in R d, where the particle can take n possible directions with different velocities and the changes of direction occur at random times, is studied.
References
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Probabilistic analysis of the telegrapher's process with drift by means of relativistic transformations
TL;DR: In this paper, the authors examined the telegrapher's process with drift and its distribution was obtained by applying the Lorentz transformation, and derived the related characteristic function as well as the distribution by solving an initial value problem for the generalized telegraph equation.
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Exact Joint Distribution In a Model of Planar Random Motion
TL;DR: In this paper, the exact joint distribution of the position of a particle performing a planar random motion with finite velocity and for possible directions (changing at Poisson times) is obtained by means of a suitable representation of the random motion in terms of independent, integrated telegraph signals.
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Exact transient analysis of a planar random motion with three directions
TL;DR: In this paper, a planar random motion with constant velocity and three directions forming the angles is considered, such that the random times between consecutive changes of direction perform an alternating renewal process, and the transition densities of the motion are expressed in terms of a suitable modified two-index Bessel function.
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Analysis of a Finite-Velocity Planar Random Motion with Reflection
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.